The Equivalence of the Convergence of Four Kinds of Iterations for a Finite Family of Uniformly Asymptotically ø-pseudocontractive Mappings
|
|
- Adrian Peters
- 6 years ago
- Views:
Transcription
1 ±39ff±1ffi ß Ω χ Vol.39, No fl2fl ADVANCES IN MATHEMATICS Feb., 2010 The Equivalence of the Convergence of Four Kinds of Iterations for a Finite Family of Uniformly Asymptotically ø-pseudocontractive Mappings WANG Xuewu (School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai, Shandong, , P. R. China) Abstract: In this paper, we prove the equivalences of the strong convergence each other the modified Mann iterative process with errors, the modified Ishikawa iterative process with errors, the implicit iterative process with errors and the composite implicit iterative process with errors for a finite family of uniformly asymptotically ø-pseudocontractive mappings in arbitrary real Banach space. The results presented in this paper generalize and improve the corresponding results of Roades, Soltuz, and Huang. Key words: uniformly asymptotically ø-pseudocontractive mapping; composite implicit iterative process; implicit iterative process; Ishikawa iterative process; Mann iterative process; equivalence MR(2000) Subject Classification: 47H05; 47H10; 47H15 / CLC number: O Document code: A Article ID: (2010) Introduction Throughout this paper, we assume that X is a real Banach space, X is the dual space of X. Let J denote the normalized duality mapping form X into 2 X given by J(x) ={f X : x, f = x 2 = f 2 } for all x X, where, denotes the generalized duality pairing. In the sequel, we shall denote the single-valued duality mapping by j. Let T 1,T 2,,T N be N self-mappings of E X and suppose that F (T )= N i=1 F (T i) Ø, the set of common fixed points of T i,i =1, 2,,N. Hereafter, we will denote the index set {1, 2,,N} by I. Mann in [1], Ishikwaw in [2], Liu in [3] and Xu in [4] introduced Mann iteration, Ishikwaw iteration and modified Mann and Ishikawa iteration with errors, respectively. Xu and Ori in [5], Sun in [6], Chang in [7] and Gu in [8] introduced an implicit iterative process, an implicit iterative process with errors and a composite implicit iterative process with errors for a finite family of mappings, respectively. In this paper, we introduced a modified Mann and Ishikawa iterative processes with errors for a finite family of mappings {T 1,T 2,,T N } as follows : For Received date: wangxuewuxx@163.com
2 80 ο Ψ ffi 39ff any given x 0 E the sequence {x n } defined by x n+1 =(1 α n γ n )x n + α n T k n y n + γ n u n,y n =(1 β n δ n )x n + β n T k n x n + δ n v n,n 0 (1) is called the modified Ishikawa iteration sequence with errors for a finite family of mappings, where {α n }, {γ n },{β n }, {δ n } are four sequences in [0, 1] satisfying the conditions α n + γ n 1 and β n + δ n 1 for all n 1, and T k = T k(mod N), n =(k 1)N + i, i I = {1, 2,,N}. In particular, if β n = δ n =0foralln 0, then {z n } defined by z 0 X, z n+1 =(1 α n γ n )z n + α n T k n z n + γ n w n, n 0 (2) is called the modified Mann iteration sequence with errors for a finite family of mappings. we also introduced a new composite implicit iterative process for a finite family of mappings as follows: x n =(1 α n γ n )x n 1 + α n Tn k y n + γ n u n, n 1; y n =(1 β n δ n )x n + β n T n k x n + δ n v n, n 1, (3) where n =(k 1)N + i, i I, T n = T n(mod N), {α n }, {β n }, {γ n}, {δ n } are four real sequences in [0, 1] satisfying α n + γ n 1andβ n + δ n 1 for all n 1, {u n}, {v n} are two sequences in E and x 0 is a given point. This sequence {x n } defined by (3) is called the composite implicit iterative sequence with errors for a finite family of mappings. Especially, if β n =0,δ n =0foralln 1, we have z n =(1 α n γ n )z n 1 + α n T k nz n + γ n w n, n 1, (4) where n =(k 1)N +i, i I, T n = T n(mod N), {α n }, {γ n } are two real sequences in [0, 1] satisfying α n + γ n 1andforalln 1, {w n} is a sequence in E and x 0 is a initial point. Huang and Bu in [9] have proved the equivalence of the convergence between the modified Mann iteration process with errors and the modified Ishikawa iteration process with errors for strongly successively pseudocontractive mapping in uniformly smooth Banach space. Rhoades and Soltuz in [11, 12] have proved the equivalence of the convergence between the original Ishikawa iterative sequence and original Mann iterative sequence under some strict conditions. Huang in [13] have established the equivalence theorems of the convergence between the modified Mann iteration process with errors and the modified Ishikawa iteration process with errors for strongly successively ø-pseudocontractives mapping without Lipschitzian assumptions in uniformly smooth Banach space. The main purpose of this paper is to study the equivalences of the convergence each other the modified Mann iterative process with errors, the modified Ishikawa iterative process with errors, the implicit iterative process with errors and the composite implicit iterative process with errors for a finite family of uniformly asymptotically ø-pseudocontractive mappings in an arbitrary real Banach space. Our results extend and improve the corresponding results presented recently in [9, 11 13] and some others.
3 1ffi»ο Ξ The Equivalence of the Convergence of Four Kinds of Iterations 81 1 Preliminaries For the sake of convenience, we first recall some definitions and conclusions. Definition 1.1 A mapping T with domain D(T ) and range R(T )inx is called asymptotically ø-pseudocontractive mapping, if for all x, y D(T ), there exist j(x y) J(x y) and a strictly increasing function ø : [0, + ) [0, + ) withø(0)=0, such that T n x T n y, j(x y) k n x y 2 ø( x y ), (5) where k n [1, + ) with lim n k n =1. Definition 1.2 A finite family of mappings {T 1,T 2,,T N } be said to be uniformly asymptotically ø-pseudocontractive mappings if for all x, y D(T )= N i=1 D(T i), there exist j(x y) J(x y) and a strictly increasing function ø : [0, + ) [0, + ) withø(0)=0, such that Tn k x T n k y, j(x y) k n x y 2 ø( x y ), (6) for all x, y X, n, k 1andj(x y) J(x y), where k n [1, + ) with lim n k n =1. Definition 1.3 A finite family of mappings {T 1,T 2,,T N } be said to be uniformly Lipschitzian, if for any x, y D(T )= N i=1 D(T i) and nonnegative integers n, thereexistsa constant L>0 such that T k nx T k n y L x y, (7) where n =(k 1)N + i, i I, T n = T n(mod N). Ramark If every T i,i I be uniformly Lipschitzian, then a finite family of mappings {T 1,T 2,,T N } be uniformly Lipschitzian. Lemma 1.1 [4] Let X be a real Banach space, and let j : X 2 X be the normalized duality mapping. Then for any x, y X we have x + y 2 x 2 +2 y, j(x + y). (8) Lemma 1.2 [14] Let {a n }, {b n }, {δ n } are three sequences of nonnegative real numbers, if there exists n 0, for all n>n 0 such that a n+1 (1 + δ n )a n + b n, (9) where n=1 δ n < and n=1 b n <. Then (i) lim n a n exists; (ii) lim n a n = 0 whenever lim inf n a n =0. Lemma 1.3 [15] Let {a n } be a sequences of positive real numbers such that n=1 a n =. Suppose that n=1 a nb n < where b n > 0 for all n 1. Then lim inf n b n =0. Lemma 1.4 Let ø : [0, ) [0, ) be a strictly increasing function with ø(0) = 0 and let {a n }, {b n }, {c n } are nonnegative real sequences such that lim n b n =0, b n =, n=1 c n <. (10) n=1
4 82 ο Ψ ffi 39ff Suppose that there exists an integer N 1 > 0 such that for all n N 1 a 2 n+1 a 2 n 2b n ø(a n+1 )+c n. (11) Then lim n a n =0. Proof Since the inequality (11) implies that a 2 n+1 a 2 n + c n. By (10) and Lemma 1.2, we have that lim n a n exists. By virtue of (11) and (10), we obtain that n=n 0 2b n ø(a n+1 ) a 2 n 0 + n=n 0 c n <, n 0 N 1. From n=1 b n = and Lemma 1.3 we have lim inf n ø(a n+1 ) = 0. In view of the properties of ø, it is obvious that lim inf n a n+1 = 0. By virtue of the conclusion (ii) in Lemma 1.2, we have lim n a n =0. 2 Main Results and Proofs Theorem 2.1 Let X be an arbitrary real Banach space and let {T 1,T 2,,T N } : X X be uniformly asymptotically ø-pseudocontractive mappings with bounded rang, and be uniformly Lipschitzian with L>0. The sequences {x n } and {z n } be defined by (1) and (2), respectively, where the sequences {u n },{v n },{w n } are bounded. If the sequences {α n },{γ n }, {β n }, {δ n } [0, 1] satisfy the following conditions: (a) n=1 γ n < ; (b) n=1 α n =, n=1 α2 n < ; (c) n=1 α nβ n <, n=1 α nδ n <, n=1 α n(k n 1) <. Then for any initial point z 0,x 0 X, the following two assertions are equivalent: (i) The modified Mann iteration sequence with errors (2) converges to common fixed x F (T ); (ii) The modified Ishikawa iteration sequence with errors (1) converges to common fixed x F (T ). Proof If the modified Ishikawa iteration sequence with errors (1) converges to common fixed x F (T ), setting β n = δ n =0, n 0, then we can get that the modified Mann iteration sequence with errors (2) converges to common fixed x F (T ). Next we will prove the result (i) (ii). Since T k n X, {x n }, {y n }, {z n }, {u n }, {v n }, {w n } are bounded, we set M =sup{ z n y n, z n x n, u n x n, v n x n, w n u n, n w n z n, Tn k x n x n, Tn k y n x n, Tn k z n z n }, (12)
5 1ffi»ο Ξ The Equivalence of the Convergence of Four Kinds of Iterations 83 obviously, M<. Form (1), (2), (12) and Lemma 1.1 we have z n+1 x n+1 2 (1 α n γ n )(z n x n )+α n (Tn k z n Tn k y n)+γ n (w n u n ) 2 (1 α n γ n ) 2 z n x n 2 +2 α n (Tn k z n Tn k y n )+γ n (w n u n ),j(z n+1 x n+1 ) (1 α n ) 2 z n x n 2 +2α n (Tn k z n+1 Tn k x n+1),j(z n+1 x n+1 ) +2α n Tn k z n Tn k y n (Tn k z n+1 Tn k x n+1 ),j(z n+1 x n+1 ) +2γ n w n u n,j(z n+1 x n+1 ) (1 α n ) 2 z n x n 2 +2α n k n z n+1 x n+1 2 2α n ø( z n+1 x n+1 ) +2α n L( z n+1 z n + x n+1 y n ) z n+1 x n+1 +2γ n w n u n z n+1 x n+1 (1 α n ) 2 z n x n 2 +2α n k n z n+1 x n+1 2 2α n ø( z n+1 x n+1 ) +2α n Mσ n +2γ n M 2, (13) where σ n = z n+1 z n + x n+1 y n. In view of (1) and (2), we have σ n = x n+1 y n + z n+1 z n α n (Tn k y n x n )+γ n (u n x n ) β n (Tn k x n x n ) δ n (v n x n ) + α n (Tn k z n z n )+γ n (w n z n ) 2M(α n + γ n + β n + δ n ). (14) From (1) and (2), we have z n+1 x n+1 = z n x n (α n + γ n )(z n x n )+α n (T k n z n T k n y n)+γ n (w n u n ), which implies that z n+1 x n+1 2 ( z n x n +(α n + γ n ) z n x n + α n Tnz k n Tn k y n + γ n w n u n ) 2 [ z n x n +((L +1)α n +2γ n )M] 2 z n x n 2 +((L +1)α n +2γ n )(2L +7)M 2. (15) Substituting (14) and (15) into (13) and simplifying, we obtain that z n+1 x n+1 2 z n x n 2 2α n ø( z n+1 x n+1 )+2α n (k n 1)M 2 +2α n Mσ n + α 2 nm 2 +2α n k n ((L +1)α n +2γ n )(2L +7)M 2 +2γ n M 2. (16) Suppose that a n = z n x n,b n = α n,c n =2α n (k n 1)M 2 +2α n Mσ n + α 2 n M 2 +2α n k n [(L + 1)α n +2γ n ](2L +7)M 2 +2γ n M 2. From (a), (b) and (c), we have that n=1 b n = and n=1 c n <. By virtue of Lemma 1.4 we obtain that lim n a n = 0. Hence lim n z n x n =0. Since the modified Mann iteration sequence with errors (2) converges to common fixed x F (T ), that is, lim n z n x = 0. From the inequality 0 x n x z n x + x n z n, we have lim n x n x = 0. This completes the proof of Theorem 2.1.
6 84 ο Ψ ffi 39ff Theorem 2.2 Let X be an arbitrary real Banach space and let {T 1,T 2,,T N } : X X be uniformly asymptotically ø-pseudocontractive mappings with bounded rang, and be uniformly Lipschitzian with L>0. The sequences {x n} and {z n} be defined by (3) and (4), respectively, where the sequences {u n }, {v n }, {w n } are bounded. If the sequences {α n}, {γ n }, {β n }, {δ n } [0, 1] satisfy the following conditions: (a) n=1 γ n < ; (b) n=1 α n =, n=1 α2 n < ; (c) n=1 α nβ n <, n=1 α nδ n <, n=1 α n(k n 1) <. Then for any initial point z 0,x 0 X, the following two assertions are equivalent: (iii) The implicit iteration sequence with errors (4) converges to common fixed x F (T ); (iv) The composite implicit iteration sequence with errors (3) converges to common fixed x F (T ). Proof If the composite implicit iteration sequences with errors (3) converges to common fixed x F (T ), taking β n = δ n =0, n 1, then we can get that implicit iteration sequence with errors (4) converges to common fixed x F (T ). Next we will prove the result (iii) (iv). Since Tn kx, {x n }, {y n }, {z n }, {u n }, {v n }, {w n } are bounded, we set M =sup{ Tnx k n x n, z n x n, z n y n, w n u n, w n v n, x n v n }, (17) n it is obvious that M<. Form (3), (4) and (17) we have z n x n 2 = (1 α n γ n )(z n 1 x n 1 )+α n(tn k z n T n k y n )+γ n(w n u n ) (1 α n γ n ) 2 z n 1 x n α n (Tn k z n Tn k y n)+γ n (w n u n),j(z n x n) (1 α n ) 2 z n 1 x n α n (Tn k z n T n k x n ),j(z n x n ) +2α n (Tn k z n Tn k y n (Tn k z n Tn k x n),j(z n x n) +2γ n w n u n,j(z n x n) (1 α n ) 2 z n 1 x n α n k n z n x n 2 2α n ø( z n x n ) +2α n Tn k x n Tn k y n z n x n +2γ n w n u n z n x n (1 α n ) 2 z n 1 x n α n k n z n x n 2 2α n ø( z n x n ) +2α n LMσ n +2γ n M 2, (18) where σ n = x n y n. Byvirtueof(3),wehave It follows from (3) and (4) that σ n = x n y n = β n (T n k x n x n )+δ n (v n x n ) β n T nx k n x n + δ n v n x n (19) (β n + δ n )M. z n x n 2 [ z n 1 x n 1 +(α n + γ n ) z n 1 x n 1 + α n T k nz n T k n y n + γ n w n u n ] 2 z n 1 x n 1 2 +[(L +1)α n +2γ n ](2L +7)M 2. (20)
7 1ffi»ο Ξ The Equivalence of the Convergence of Four Kinds of Iterations 85 Substituting (19) and (20) into (18) and simplifying, we have z n x n 2 z n 1 x n 1 2 2α n ø( z n x n )+2α n (k n 1)M 2 +2LMα n σ n + α 2 n M 2 +2α n k n [(L +1)α n +2γ n ](2L +7)M 2 +2γ n M 2. (21) Suppose that a n = z n x n,b n = α n,c n =2α n (k n 1)M 2 +2LMα n σ n + α 2 n M 2 +2α n k n [(L + 1)α n +2γ n ](2L +7)M 2 +2γ n M 2. By (a), (b) and (c) we have n=1 b n = and n=1 c n <. By virtue of Lemma 1.4 we obtain that lim n a n =0. Hence lim n z n x n =0. Since implicit iteration sequence with errors (4) converges to common fixed x F (T ), that is, lim n z n x = 0. From the inequality 0 x n x z n x + x n z n,wehave lim n x n x = 0. This completes the proof of Theorem 2.2. Theorem 2.3 Let X be an arbitrary real Banach space and let {T 1,T 2,,T N } : X X be uniformly asymptotically ø-pseudocontractive mappings with bounded rang, and be uniformly Lipschitzian with L>0. The sequences {z n } and {z n } be defined by (2) and (4), respectively, where the sequences {w n }, {w n} are bounded. The sequences {α n },{γ n } [0, 1] satisfy the following conditions: (a) n=1 γ n < ; (b) n=1 α n =, n=1 α2 n <, n=1 α n(k n 1) <. Then for any initial point z 0,z 0 X, the following two assertions are equivalent: (v) The implicit iteration sequence with errors (4) converges to common fixed x F (T ); (vi) The modified Mann iteration sequence with errors (2) converges to common fixed x F (T ). Proof Since Tn kx, {z n}, {z n }, {w n}, {w n } are bounded, we set M =sup{ Tnz k n z n, z n+1 z n, w n w n, z n w n, z n z n }, (22) n obviously, M<. From (2), (4) and (22), we have z n+1 z n 2 (1 α n γ n )(z n z n 1 )+α n(t k n z n T k n z n )+γ n(w n w n ) 2 (1 α n γ n ) 2 z n z n α n (Tn k z n Tn k z n)+γ n (w n w n),j(z n+1 z n) (1 α n ) 2 z n z n α n (Tn k z n+1 Tn k z n ),j(z n+1 z n ) +2α n Tn k z n Tn k z n (Tn k z n+1 Tn k z n),j(z n+1 z n)) +2γ n w n w n,j(z n+1 z n) (1 α n ) 2 z n z n α n k n z n+1 z n 2 2α n ø( z n+1 z n ) +2α n LMσ n +2γ n M 2, (23) where σ n = z n+1 z n.byvirtueof(2),wehave By (2) and (4) we have that σ n = z n+1 z n α n T k n z n z n + γ n z n w n (α n + γ n )M. (24) z n+1 z n =(1 α n γ n )(z n z n 1)+α n (Tn k z n Tn k z n)+γ n (w n w n) =(z n z n 1 ) (α n + γ n )(z n z n 1 )+α n(tn k z n Tn k z n )+γ n(w n w n ).
8 86 ο Ψ ffi 39ff Therefore we have z n+1 z n 2 z n z n 1 2 +[(L +1)α n +2γ n ](2L +7)M 2. (25) Substituting (25) and (24) into (23) and simplifying, we obtain that z n+1 z n 2 z n z n 1 2 2α n ø( z n+1 z n )+2α n (k n 1)M +2α n k n [(L +1)α n +2γ n ](2L +7)M 2 +2α n LMσ n +2γ n M 2. (26) Let a n = z n+1 z n,b n = α n,c n =2α n (k n 1)M +2α n k n [(L +1)α n +2γ n ](2L +7)M 2 + 2α n LMσ n +2γ n M 2. By (a) and (b) we have n=1 b n =, n=1 c n <. By virtue of Lemma 1.4 we obtain that lim n a n = 0. That is, lim n z n+1 z n =0. If implicit iteration sequence with errors (4) converges to common fixed z F (T ), that is, lim n z n z = 0. From the inequality 0 z n+1 z z n z + z n+1 z n we have lim n z n+1 z = 0. Conversely, if the Mann iteration sequence with errors (2) converges to common fixed z F (T ), that is, lim n z n+1 z = 0. From the inequality 0 z n z z n+1 x + z n+1 z n,wehavelim n z n z = 0. This completes the proof of Theorem 2.3. Theorem 2.4 Let X be an arbitrary real Banach space and let {T 1,T 2,,T N } : X X be uniformly asymptotically ø-pseudocontractive mappings with bounded rang, and be uniformly Lipschitzian with L>0. The sequences {x n } and {x n} be defined by (1) and (3), respectively, where the sequences {u n }, {v n }, {w n }, {u n }, {v n }, {w n } are bounded. If the sequences {α n}, {γ n }, {β n }, {δ n }, {β n}, {δ n} [0, 1] satisfy the following conditions: (a) n=1 γ n < ; (b) n=1 α n =, n=1 α2 n < ; (c) n=1 α nβ n <, n=1 α nδ n <, n=1 α n(k n 1) <. (d) n=1 α nβ n <, n=1 α nδ n <. Then for any initial point z 0,x 0 X, the following two assertions are equivalent: (vii) The modified Ishikawa iteration sequence with errors (1) converges to common fixed x F (T ); (viii) The composite implicit iteration sequence with errors (3) converges to common fixed x F (T ). Proof By virtue of the conclusions of Theorem 2.1, Theorem 2.2 and Theorem 2.3, we obtain that (i) (ii), (iii) (iv) and (v) (vi). Again from (i) and (vii), (ii) and (v), (iii) and (v), (iv) and (vi) are the same, respectively. Therefore, we have that (viii) (vii). This completes the proof of Theorem 2.4. References [1] Ishikawa, S., Fixed point and iteration of a nonexpansive mapping in a Banach spaces, Proc. Amer. Math. Soc., 1976, 73: [2] Mann, W.R., Mean value methods in iteration, Proc. Amer. Math. Soc., 1953, 4:
9 1ffi»ο Ξ The Equivalence of the Convergence of Four Kinds of Iterations 87 [3] Liu L.S., Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mapping in Banach spaces, J. Math. Anal. Appl., 1995, 194: [4] Xu Y.G., Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl., 1998, 224: [5] Xu H.K., Ori, R.G., An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim., 2001, 22: [6] Sun Z.H., Strong convergence of an implicit iteration process for a finite family of asymptotically quasinonexpansive mappings, J. Math. Anal. Appl., 2003, 286: [7] Chang S.S., Tan K.K., et al, On the convergence of implicit iteration process with error for a finit family of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 2006, 313: [8] Gu F., The new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings, J. Math. Anal. Appl., 2007, 294: [9] Huang Z.Y., Bu F.W., The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption, J. Math. Anal. Appl., 2007, 325: [10] Agarwal, R.P., Cho, Y.J., Stability of iterative procedures with errors approximating common fixed points for a couple of qusi-contrative mapping in q-uniformly smooth Banach spaces, J. Math. Anal. Appl., 2002, 272: [11] Roades, B.E., Soltuz, S.M., The equivalence between the convergence of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps, J. Math. Anal. Appl., 20024, 289: [12] Roades, B.E., Soltuz, S.M., The equivalence between Mann-Ishikawa iterations and multi-step iteration, Nonlinear Anal., 2004, 58: [13] Huang Z.Y., Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively ø-pseudocontractive mappings without Lipschitzian assumption, J. Math. Anal. Appl., 2007, 329: [14] Tan K.K., Xu H.K., Approximating fixed points of nonexpansive mappings by the Ishikawa iterative process, J. Math. Anal. Appl., 1993, 178: [15] Ofoedu, E.U., Strong convergence theorem for uniformly L-Lipschitzan asymptotically pseudocontractive mapping in real Banach space, J. Math. Anal. Appl., 2006, 321: &:91>7<)* ø- 05/82".=$!4,-+"#'3?A@ (ffl Φ οfi οffνμfiοοfi ρ ffl ) ;6Λ Bev[Zt^nG Banach XR_GKsrgxmwSU ø- dlbqigwf CGku Mann IFNE WfCGku Ishikwaw IFNE WfCGo`IFNEOWfC GPDo`IFNEaYGHQj TMcLOJUZ Roades, Soltuz O Huang H]Ghp TM %(ψλ mwsv ø- dlbqiπpdo`ifneπo`ifneπ Ishikwaw IFN EΠ Mann IFNEΠHQ
STRONG CONVERGENCE OF AN IMPLICIT ITERATION PROCESS FOR ASYMPTOTICALLY NONEXPANSIVE IN THE INTERMEDIATE SENSE MAPPINGS IN BANACH SPACES
Kragujevac Journal of Mathematics Volume 36 Number 2 (2012), Pages 237 249. STRONG CONVERGENCE OF AN IMPLICIT ITERATION PROCESS FOR ASYMPTOTICALLY NONEXPANSIVE IN THE INTERMEDIATE SENSE MAPPINGS IN BANACH
More informationCONVERGENCE OF HYBRID FIXED POINT FOR A PAIR OF NONLINEAR MAPPINGS IN BANACH SPACES
International Journal of Analysis and Applications ISSN 2291-8639 Volume 8, Number 1 2015), 69-78 http://www.etamaths.com CONVERGENCE OF HYBRID FIXED POINT FOR A PAIR OF NONLINEAR MAPPINGS IN BANACH SPACES
More informationOn The Convergence Of Modified Noor Iteration For Nearly Lipschitzian Maps In Real Banach Spaces
CJMS. 2(2)(2013), 95-104 Caspian Journal of Mathematical Sciences (CJMS) University of Mazandaran, Iran http://cjms.journals.umz.ac.ir ISSN: 1735-0611 On The Convergence Of Modified Noor Iteration For
More informationON THE CONVERGENCE OF MODIFIED NOOR ITERATION METHOD FOR NEARLY LIPSCHITZIAN MAPPINGS IN ARBITRARY REAL BANACH SPACES
TJMM 6 (2014), No. 1, 45-51 ON THE CONVERGENCE OF MODIFIED NOOR ITERATION METHOD FOR NEARLY LIPSCHITZIAN MAPPINGS IN ARBITRARY REAL BANACH SPACES ADESANMI ALAO MOGBADEMU Abstract. In this present paper,
More informationFIXED POINT ITERATION FOR PSEUDOCONTRACTIVE MAPS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 127, Number 4, April 1999, Pages 1163 1170 S 0002-9939(99)05050-9 FIXED POINT ITERATION FOR PSEUDOCONTRACTIVE MAPS C. E. CHIDUME AND CHIKA MOORE
More informationReceived 8 June 2003 Submitted by Z.-J. Ruan
J. Math. Anal. Appl. 289 2004) 266 278 www.elsevier.com/locate/jmaa The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense
More informationSTRONG CONVERGENCE RESULTS FOR NEARLY WEAK UNIFORMLY L-LIPSCHITZIAN MAPPINGS
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org / JOURNALS / BULLETIN Vol. 6(2016), 199-208 Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS
More informationConvergence to Common Fixed Point for Two Asymptotically Quasi-nonexpansive Mappings in the Intermediate Sense in Banach Spaces
Mathematica Moravica Vol. 19-1 2015, 33 48 Convergence to Common Fixed Point for Two Asymptotically Quasi-nonexpansive Mappings in the Intermediate Sense in Banach Spaces Gurucharan Singh Saluja Abstract.
More informationCONVERGENCE THEOREMS FOR STRICTLY ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS IN HILBERT SPACES. Gurucharan Singh Saluja
Opuscula Mathematica Vol 30 No 4 2010 http://dxdoiorg/107494/opmath2010304485 CONVERGENCE THEOREMS FOR STRICTLY ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS IN HILBERT SPACES Gurucharan Singh Saluja Abstract
More informationThe equivalence of Picard, Mann and Ishikawa iterations dealing with quasi-contractive operators
Mathematical Communications 10(2005), 81-88 81 The equivalence of Picard, Mann and Ishikawa iterations dealing with quasi-contractive operators Ştefan M. Şoltuz Abstract. We show that the Ishikawa iteration,
More informationStrong Convergence Theorems for Nonself I-Asymptotically Quasi-Nonexpansive Mappings 1
Applied Mathematical Sciences, Vol. 2, 2008, no. 19, 919-928 Strong Convergence Theorems for Nonself I-Asymptotically Quasi-Nonexpansive Mappings 1 Si-Sheng Yao Department of Mathematics, Kunming Teachers
More informationShih-sen Chang, Yeol Je Cho, and Haiyun Zhou
J. Korean Math. Soc. 38 (2001), No. 6, pp. 1245 1260 DEMI-CLOSED PRINCIPLE AND WEAK CONVERGENCE PROBLEMS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS Shih-sen Chang, Yeol Je Cho, and Haiyun Zhou Abstract.
More informationCommon fixed points of two generalized asymptotically quasi-nonexpansive mappings
An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) Tomul LXIII, 2017, f. 2 Common fixed points of two generalized asymptotically quasi-nonexpansive mappings Safeer Hussain Khan Isa Yildirim Received: 5.VIII.2013
More informationViscosity Iterative Approximating the Common Fixed Points of Non-expansive Semigroups in Banach Spaces
Viscosity Iterative Approximating the Common Fixed Points of Non-expansive Semigroups in Banach Spaces YUAN-HENG WANG Zhejiang Normal University Department of Mathematics Yingbing Road 688, 321004 Jinhua
More informationStrong convergence of multi-step iterates with errors for generalized asymptotically quasi-nonexpansive mappings
Palestine Journal of Mathematics Vol. 1 01, 50 64 Palestine Polytechnic University-PPU 01 Strong convergence of multi-step iterates with errors for generalized asymptotically quasi-nonexpansive mappings
More informationHAIYUN ZHOU, RAVI P. AGARWAL, YEOL JE CHO, AND YONG SOO KIM
Georgian Mathematical Journal Volume 9 (2002), Number 3, 591 600 NONEXPANSIVE MAPPINGS AND ITERATIVE METHODS IN UNIFORMLY CONVEX BANACH SPACES HAIYUN ZHOU, RAVI P. AGARWAL, YEOL JE CHO, AND YONG SOO KIM
More informationConvergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 2016), 5119 5135 Research Article Convergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense Gurucharan
More informationON WEAK AND STRONG CONVERGENCE THEOREMS FOR TWO NONEXPANSIVE MAPPINGS IN BANACH SPACES. Pankaj Kumar Jhade and A. S. Saluja
MATEMATIQKI VESNIK 66, 1 (2014), 1 8 March 2014 originalni nauqni rad research paper ON WEAK AND STRONG CONVERGENCE THEOREMS FOR TWO NONEXPANSIVE MAPPINGS IN BANACH SPACES Pankaj Kumar Jhade and A. S.
More informationWeak and strong convergence theorems of modified SP-iterations for generalized asymptotically quasi-nonexpansive mappings
Mathematica Moravica Vol. 20:1 (2016), 125 144 Weak and strong convergence theorems of modified SP-iterations for generalized asymptotically quasi-nonexpansive mappings G.S. Saluja Abstract. The aim of
More informationAPPROXIMATING SOLUTIONS FOR THE SYSTEM OF REFLEXIVE BANACH SPACE
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 2 Issue 3(2010), Pages 32-39. APPROXIMATING SOLUTIONS FOR THE SYSTEM OF φ-strongly ACCRETIVE OPERATOR
More informationWeak and strong convergence of a scheme with errors for three nonexpansive mappings
Rostock. Math. Kolloq. 63, 25 35 (2008) Subject Classification (AMS) 47H09, 47H10 Daruni Boonchari, Satit Saejung Weak and strong convergence of a scheme with errors for three nonexpansive mappings ABSTRACT.
More informationTwo-Step Iteration Scheme for Nonexpansive Mappings in Banach Space
Mathematica Moravica Vol. 19-1 (2015), 95 105 Two-Step Iteration Scheme for Nonexpansive Mappings in Banach Space M.R. Yadav Abstract. In this paper, we introduce a new two-step iteration process to approximate
More informationConvergence of Ishikawa Iterative Sequances for Lipschitzian Strongly Pseudocontractive Operator
Australian Journal of Basic Applied Sciences, 5(11): 602-606, 2011 ISSN 1991-8178 Convergence of Ishikawa Iterative Sequances for Lipschitzian Strongly Pseudocontractive Operator D. Behmardi, L. Shirazi
More informationInternational Journal of Scientific & Engineering Research, Volume 7, Issue 12, December-2016 ISSN
1750 Approximation of Fixed Points of Multivalued Demicontractive and Multivalued Hemicontractive Mappings in Hilbert Spaces B. G. Akuchu Department of Mathematics University of Nigeria Nsukka e-mail:
More informationSteepest descent approximations in Banach space 1
General Mathematics Vol. 16, No. 3 (2008), 133 143 Steepest descent approximations in Banach space 1 Arif Rafiq, Ana Maria Acu, Mugur Acu Abstract Let E be a real Banach space and let A : E E be a Lipschitzian
More informationWeak and Strong Convergence Theorems for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Nonself-Mappings
Int. J. Nonlinear Anal. Appl. 3 (2012) No. 1, 9-16 ISSN: 2008-6822 (electronic) http://www.ijnaa.semnan.ac.ir Weak and Strong Convergence Theorems for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive
More informationBulletin of the Iranian Mathematical Society Vol. 39 No.6 (2013), pp
Bulletin of the Iranian Mathematical Society Vol. 39 No.6 (2013), pp 1125-1135. COMMON FIXED POINTS OF A FINITE FAMILY OF MULTIVALUED QUASI-NONEXPANSIVE MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES A. BUNYAWAT
More informationSHRINKING PROJECTION METHOD FOR A SEQUENCE OF RELATIVELY QUASI-NONEXPANSIVE MULTIVALUED MAPPINGS AND EQUILIBRIUM PROBLEM IN BANACH SPACES
U.P.B. Sci. Bull., Series A, Vol. 76, Iss. 2, 2014 ISSN 1223-7027 SHRINKING PROJECTION METHOD FOR A SEQUENCE OF RELATIVELY QUASI-NONEXPANSIVE MULTIVALUED MAPPINGS AND EQUILIBRIUM PROBLEM IN BANACH SPACES
More informationApproximating Fixed Points of Asymptotically Quasi-Nonexpansive Mappings by the Iterative Sequences with Errors
5 10 July 2004, Antalya, Turkey Dynamical Systems and Applications, Proceedings, pp. 262 272 Approximating Fixed Points of Asymptotically Quasi-Nonexpansive Mappings by the Iterative Sequences with Errors
More informationThe convergence of Mann iteration with errors is equivalent to the convergence of Ishikawa iteration with errors
This is a reprint of Lecturas Matemáticas Volumen 25 (2004), páginas 5 13 The convergence of Mann iteration with errors is equivalent to the convergence of Ishikawa iteration with errors Stefan M. Şoltuz
More informationOn the approximation problem of common fixed points for a finite family of non-self asymptotically quasi-nonexpansive-type mappings in Banach spaces
Computers and Mathematics with Applications 53 (2007) 1847 1853 www.elsevier.com/locate/camwa On the approximation problem of common fixed points for a finite family of non-self asymptotically quasi-nonexpansive-type
More informationViscosity approximation method for m-accretive mapping and variational inequality in Banach space
An. Şt. Univ. Ovidius Constanţa Vol. 17(1), 2009, 91 104 Viscosity approximation method for m-accretive mapping and variational inequality in Banach space Zhenhua He 1, Deifei Zhang 1, Feng Gu 2 Abstract
More informationON WEAK CONVERGENCE THEOREM FOR NONSELF I-QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
BULLETIN OF INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN 1840-4367 Vol. 2(2012), 69-75 Former BULLETIN OF SOCIETY OF MATHEMATICIANS BANJA LUKA ISSN 0354-5792 (o), ISSN 1986-521X (p) ON WEAK CONVERGENCE
More informationON A HYBRID PROXIMAL POINT ALGORITHM IN BANACH SPACES
U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 3, 2018 ISSN 1223-7027 ON A HYBRID PROXIMAL POINT ALGORITHM IN BANACH SPACES Vahid Dadashi 1 In this paper, we introduce a hybrid projection algorithm for a countable
More informationCONVERGENCE OF THE STEEPEST DESCENT METHOD FOR ACCRETIVE OPERATORS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 127, Number 12, Pages 3677 3683 S 0002-9939(99)04975-8 Article electronically published on May 11, 1999 CONVERGENCE OF THE STEEPEST DESCENT METHOD
More informationOn nonexpansive and accretive operators in Banach spaces
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 3437 3446 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa On nonexpansive and accretive
More informationResearch Article Convergence Theorems for Common Fixed Points of Nonself Asymptotically Quasi-Non-Expansive Mappings
Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008, Article ID 428241, 11 pages doi:10.1155/2008/428241 Research Article Convergence Theorems for Common Fixed Points of Nonself
More informationCONVERGENCE THEOREMS FOR TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
An. Şt. Univ. Ovidius Constanţa Vol. 18(1), 2010, 163 180 CONVERGENCE THEOREMS FOR TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS Yan Hao Abstract In this paper, a demiclosed principle for total asymptotically
More informationViscosity approximation methods for nonexpansive nonself-mappings
J. Math. Anal. Appl. 321 (2006) 316 326 www.elsevier.com/locate/jmaa Viscosity approximation methods for nonexpansive nonself-mappings Yisheng Song, Rudong Chen Department of Mathematics, Tianjin Polytechnic
More informationOn the Convergence of Ishikawa Iterates to a Common Fixed Point for a Pair of Nonexpansive Mappings in Banach Spaces
Mathematica Moravica Vol. 14-1 (2010), 113 119 On the Convergence of Ishikawa Iterates to a Common Fixed Point for a Pair of Nonexpansive Mappings in Banach Spaces Amit Singh and R.C. Dimri Abstract. In
More informationConvergence Rates in Regularization for Nonlinear Ill-Posed Equations Involving m-accretive Mappings in Banach Spaces
Applied Mathematical Sciences, Vol. 6, 212, no. 63, 319-3117 Convergence Rates in Regularization for Nonlinear Ill-Posed Equations Involving m-accretive Mappings in Banach Spaces Nguyen Buong Vietnamese
More informationOn an iterative algorithm for variational inequalities in. Banach space
MATHEMATICAL COMMUNICATIONS 95 Math. Commun. 16(2011), 95 104. On an iterative algorithm for variational inequalities in Banach spaces Yonghong Yao 1, Muhammad Aslam Noor 2,, Khalida Inayat Noor 3 and
More informationCONVERGENCE THEOREMS FOR MULTI-VALUED MAPPINGS. 1. Introduction
CONVERGENCE THEOREMS FOR MULTI-VALUED MAPPINGS YEKINI SHEHU, G. C. UGWUNNADI Abstract. In this paper, we introduce a new iterative process to approximate a common fixed point of an infinite family of multi-valued
More informationarxiv: v1 [math.fa] 15 Apr 2017 Fixed Point of A New Type Nonself Total Asymptotically Nonexpansive Mappings in Banach Spaces
arxiv:1704.04625v1 [math.fa] 15 Apr 2017 Fixed Point of A New Type Nonself Total Asymptotically Nonexpansive Mappings in Banach Spaces Birol GUNDUZ, Hemen DUTTA, and Adem KILICMAN Abstract. In this work,
More informationAlfred O. Bosede NOOR ITERATIONS ASSOCIATED WITH ZAMFIRESCU MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES
F A S C I C U L I M A T H E M A T I C I Nr 42 2009 Alfred O. Bosede NOOR ITERATIONS ASSOCIATED WITH ZAMFIRESCU MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES Abstract. In this paper, we establish some fixed
More information1. Introduction A SYSTEM OF NONCONVEX VARIATIONAL INEQUALITIES IN BANACH SPACES
Commun. Optim. Theory 2016 (2016), Article ID 20 Copyright c 2016 Mathematical Research Press. A SYSTEM OF NONCONVEX VARIATIONAL INEQUALITIES IN BANACH SPACES JONG KYU KIM 1, SALAHUDDIN 2, 1 Department
More informationIterative common solutions of fixed point and variational inequality problems
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 1882 1890 Research Article Iterative common solutions of fixed point and variational inequality problems Yunpeng Zhang a, Qing Yuan b,
More informationThe Journal of Nonlinear Science and Applications
J. Nonlinear Sci. Appl. 2 (2009), no. 2, 78 91 The Journal of Nonlinear Science and Applications http://www.tjnsa.com STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF STRICT
More informationOn the split equality common fixed point problem for quasi-nonexpansive multi-valued mappings in Banach spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (06), 5536 5543 Research Article On the split equality common fixed point problem for quasi-nonexpansive multi-valued mappings in Banach spaces
More informationSTRONG CONVERGENCE OF A MODIFIED ISHIKAWA ITERATIVE ALGORITHM FOR LIPSCHITZ PSEUDOCONTRACTIVE MAPPINGS
J. Appl. Math. & Informatics Vol. 3(203), No. 3-4, pp. 565-575 Website: http://www.kcam.biz STRONG CONVERGENCE OF A MODIFIED ISHIKAWA ITERATIVE ALGORITHM FOR LIPSCHITZ PSEUDOCONTRACTIVE MAPPINGS M.O. OSILIKE,
More informationStrong convergence theorems for total quasi-ϕasymptotically
RESEARCH Open Access Strong convergence theorems for total quasi-ϕasymptotically nonexpansive multi-valued mappings in Banach spaces Jinfang Tang 1 and Shih-sen Chang 2* * Correspondence: changss@yahoo.
More informationA Relaxed Explicit Extragradient-Like Method for Solving Generalized Mixed Equilibria, Variational Inequalities and Constrained Convex Minimization
, March 16-18, 2016, Hong Kong A Relaxed Explicit Extragradient-Like Method for Solving Generalized Mixed Equilibria, Variational Inequalities and Constrained Convex Minimization Yung-Yih Lur, Lu-Chuan
More informationSynchronal Algorithm For a Countable Family of Strict Pseudocontractions in q-uniformly Smooth Banach Spaces
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 15, 727-745 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.212287 Synchronal Algorithm For a Countable Family of Strict Pseudocontractions
More informationConvergence Theorems of Approximate Proximal Point Algorithm for Zeroes of Maximal Monotone Operators in Hilbert Spaces 1
Int. Journal of Math. Analysis, Vol. 1, 2007, no. 4, 175-186 Convergence Theorems of Approximate Proximal Point Algorithm for Zeroes of Maximal Monotone Operators in Hilbert Spaces 1 Haiyun Zhou Institute
More informationResearch Article Iterative Approximation of a Common Zero of a Countably Infinite Family of m-accretive Operators in Banach Spaces
Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008, Article ID 325792, 13 pages doi:10.1155/2008/325792 Research Article Iterative Approximation of a Common Zero of a Countably
More informationResearch Article Iterative Approximation of Common Fixed Points of Two Nonself Asymptotically Nonexpansive Mappings
Discrete Dynamics in Nature and Society Volume 2011, Article ID 487864, 16 pages doi:10.1155/2011/487864 Research Article Iterative Approximation of Common Fixed Points of Two Nonself Asymptotically Nonexpansive
More informationITERATIVE APPROXIMATION OF SOLUTIONS OF GENERALIZED EQUATIONS OF HAMMERSTEIN TYPE
Fixed Point Theory, 15(014), No., 47-440 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html ITERATIVE APPROXIMATION OF SOLUTIONS OF GENERALIZED EQUATIONS OF HAMMERSTEIN TYPE C.E. CHIDUME AND Y. SHEHU Mathematics
More informationRegularization Inertial Proximal Point Algorithm for Convex Feasibility Problems in Banach Spaces
Int. Journal of Math. Analysis, Vol. 3, 2009, no. 12, 549-561 Regularization Inertial Proximal Point Algorithm for Convex Feasibility Problems in Banach Spaces Nguyen Buong Vietnamse Academy of Science
More informationThe Split Common Fixed Point Problem for Asymptotically Quasi-Nonexpansive Mappings in the Intermediate Sense
International Mathematical Forum, Vol. 8, 2013, no. 25, 1233-1241 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2013.3599 The Split Common Fixed Point Problem for Asymptotically Quasi-Nonexpansive
More informationWeak and strong convergence of an explicit iteration process for an asymptotically quasi-i-nonexpansive mapping in Banach spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 5 (2012), 403 411 Research Article Weak and strong convergence of an explicit iteration process for an asymptotically quasi-i-nonexpansive mapping
More informationResearch Article Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces
Abstract and Applied Analysis Volume 2012, Article ID 435790, 6 pages doi:10.1155/2012/435790 Research Article Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly
More informationTHROUGHOUT this paper, we let C be a nonempty
Strong Convergence Theorems of Multivalued Nonexpansive Mappings and Maximal Monotone Operators in Banach Spaces Kriengsak Wattanawitoon, Uamporn Witthayarat and Poom Kumam Abstract In this paper, we prove
More informationGraph Convergence for H(, )-co-accretive Mapping with over-relaxed Proximal Point Method for Solving a Generalized Variational Inclusion Problem
Iranian Journal of Mathematical Sciences and Informatics Vol. 12, No. 1 (2017), pp 35-46 DOI: 10.7508/ijmsi.2017.01.004 Graph Convergence for H(, )-co-accretive Mapping with over-relaxed Proximal Point
More informationFixed Points of Multivalued Quasi-nonexpansive Mappings Using a Faster Iterative Process
Fixed Points of Multivalued Quasi-nonexpansive Mappings Using a Faster Iterative Process Safeer Hussain KHAN Department of Mathematics, Statistics and Physics, Qatar University, Doha 73, Qatar E-mail :
More informationThe Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in Hilbert Spaces
Applied Mathematical Sciences, Vol. 11, 2017, no. 12, 549-560 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.718 The Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive
More informationDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2009, Article ID 728510, 14 pages doi:10.1155/2009/728510 Research Article Common Fixed Points of Multistep Noor Iterations with Errors
More informationASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN MODULAR FUNCTION SPACES ABSTRACT
ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN MODULAR FUNCTION SPACES T. DOMINGUEZ-BENAVIDES, M.A. KHAMSI AND S. SAMADI ABSTRACT In this paper, we prove that if ρ is a convex, σ-finite modular function satisfying
More informationA Viscosity Method for Solving a General System of Finite Variational Inequalities for Finite Accretive Operators
A Viscosity Method for Solving a General System of Finite Variational Inequalities for Finite Accretive Operators Phayap Katchang, Somyot Plubtieng and Poom Kumam Member, IAENG Abstract In this paper,
More informationSTRONG CONVERGENCE OF AN ITERATIVE METHOD FOR VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS
ARCHIVUM MATHEMATICUM (BRNO) Tomus 45 (2009), 147 158 STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS Xiaolong Qin 1, Shin Min Kang 1, Yongfu Su 2,
More informationA general iterative algorithm for equilibrium problems and strict pseudo-contractions in Hilbert spaces
A general iterative algorithm for equilibrium problems and strict pseudo-contractions in Hilbert spaces MING TIAN College of Science Civil Aviation University of China Tianjin 300300, China P. R. CHINA
More informationSTRONG CONVERGENCE THEOREMS BY A HYBRID STEEPEST DESCENT METHOD FOR COUNTABLE NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Scientiae Mathematicae Japonicae Online, e-2008, 557 570 557 STRONG CONVERGENCE THEOREMS BY A HYBRID STEEPEST DESCENT METHOD FOR COUNTABLE NONEXPANSIVE MAPPINGS IN HILBERT SPACES SHIGERU IEMOTO AND WATARU
More informationStrong convergence theorems for asymptotically nonexpansive nonself-mappings with applications
Guo et al. Fixed Point Theory and Applications (2015) 2015:212 DOI 10.1186/s13663-015-0463-6 R E S E A R C H Open Access Strong convergence theorems for asymptotically nonexpansive nonself-mappings with
More informationMonotone variational inequalities, generalized equilibrium problems and fixed point methods
Wang Fixed Point Theory and Applications 2014, 2014:236 R E S E A R C H Open Access Monotone variational inequalities, generalized equilibrium problems and fixed point methods Shenghua Wang * * Correspondence:
More informationON THE CONVERGENCE OF THE ISHIKAWA ITERATION IN THE CLASS OF QUASI CONTRACTIVE OPERATORS. 1. Introduction
Acta Math. Univ. Comenianae Vol. LXXIII, 1(2004), pp. 119 126 119 ON THE CONVERGENCE OF THE ISHIKAWA ITERATION IN THE CLASS OF QUASI CONTRACTIVE OPERATORS V. BERINDE Abstract. A convergence theorem of
More informationConvergence theorems for a finite family. of nonspreading and nonexpansive. multivalued mappings and equilibrium. problems with application
Theoretical Mathematics & Applications, vol.3, no.3, 2013, 49-61 ISSN: 1792-9687 (print), 1792-9709 (online) Scienpress Ltd, 2013 Convergence theorems for a finite family of nonspreading and nonexpansive
More informationFixed point theory for nonlinear mappings in Banach spaces and applications
Kangtunyakarn Fixed Point Theory and Applications 014, 014:108 http://www.fixedpointtheoryandapplications.com/content/014/1/108 R E S E A R C H Open Access Fixed point theory for nonlinear mappings in
More informationStrong convergence theorems for two total asymptotically nonexpansive nonself mappings in Banach spaces
Kiziltunc and Yolacan Fixed Point Theory and Applications 2013, 2013:90 R E S E A R C H Open Access Strong convergence theorems for two total asymptotically nonexpansive nonself mappings in Banach spaces
More informationA NEW COMPOSITE IMPLICIT ITERATIVE PROCESS FOR A FINITE FAMILY OF NONEXPANSIVE MAPPINGS IN BANACH SPACES
A NEW COMPOSITE IMPLICIT ITERATIVE PROCESS FOR A FINITE FAMILY OF NONEXPANSIVE MAPPINGS IN BANACH SPACES FENG GU AND JING LU Received 18 January 2006; Revised 22 August 2006; Accepted 23 August 2006 The
More informationOn a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis
Available online at wwwtjnsacom J Nonlinear Sci Appl 9 (2016), 2553 2562 Research Article On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis Wutiphol
More informationFixed points of Ćirić quasi-contractive operators in normed spaces
Mathematical Communications 11(006), 115-10 115 Fixed points of Ćirić quasi-contractive operators in normed spaces Arif Rafiq Abstract. We establish a general theorem to approximate fixed points of Ćirić
More informationITERATIVE SCHEMES FOR APPROXIMATING SOLUTIONS OF ACCRETIVE OPERATORS IN BANACH SPACES SHOJI KAMIMURA AND WATARU TAKAHASHI. Received December 14, 1999
Scientiae Mathematicae Vol. 3, No. 1(2000), 107 115 107 ITERATIVE SCHEMES FOR APPROXIMATING SOLUTIONS OF ACCRETIVE OPERATORS IN BANACH SPACES SHOJI KAMIMURA AND WATARU TAKAHASHI Received December 14, 1999
More informationSome unified algorithms for finding minimum norm fixed point of nonexpansive semigroups in Hilbert spaces
An. Şt. Univ. Ovidius Constanţa Vol. 19(1), 211, 331 346 Some unified algorithms for finding minimum norm fixed point of nonexpansive semigroups in Hilbert spaces Yonghong Yao, Yeong-Cheng Liou Abstract
More informationViscosity Approximative Methods for Nonexpansive Nonself-Mappings without Boundary Conditions in Banach Spaces
Applied Mathematical Sciences, Vol. 2, 2008, no. 22, 1053-1062 Viscosity Approximative Methods for Nonexpansive Nonself-Mappings without Boundary Conditions in Banach Spaces Rabian Wangkeeree and Pramote
More informationResearch Article A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings
Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2009, Article ID 615107, 17 pages doi:10.1155/2009/615107 Research Article A New Iteration Process for
More informationResearch Article Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications
Abstract and Applied Analysis Volume 2012, Article ID 479438, 13 pages doi:10.1155/2012/479438 Research Article Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and
More informationCONVERGENCE OF APPROXIMATING FIXED POINTS FOR MULTIVALUED NONSELF-MAPPINGS IN BANACH SPACES. Jong Soo Jung. 1. Introduction
Korean J. Math. 16 (2008), No. 2, pp. 215 231 CONVERGENCE OF APPROXIMATING FIXED POINTS FOR MULTIVALUED NONSELF-MAPPINGS IN BANACH SPACES Jong Soo Jung Abstract. Let E be a uniformly convex Banach space
More informationRenormings of c 0 and the minimal displacement problem
doi: 0.55/umcsmath-205-0008 ANNALES UNIVERSITATIS MARIAE CURIE-SKŁODOWSKA LUBLIN POLONIA VOL. LXVIII, NO. 2, 204 SECTIO A 85 9 ŁUKASZ PIASECKI Renormings of c 0 and the minimal displacement problem Abstract.
More informationWEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Applicable Analysis and Discrete Mathematics available online at http://pemath.et.b.ac.yu Appl. Anal. Discrete Math. 2 (2008), 197 204. doi:10.2298/aadm0802197m WEAK AND STRONG CONVERGENCE OF AN ITERATIVE
More informationA FIXED POINT THEOREM FOR GENERALIZED NONEXPANSIVE MULTIVALUED MAPPINGS
Fixed Point Theory, (0), No., 4-46 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html A FIXED POINT THEOREM FOR GENERALIZED NONEXPANSIVE MULTIVALUED MAPPINGS A. ABKAR AND M. ESLAMIAN Department of Mathematics,
More informationStrong Convergence of the Mann Iteration for Demicontractive Mappings
Applied Mathematical Sciences, Vol. 9, 015, no. 4, 061-068 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.015.5166 Strong Convergence of the Mann Iteration for Demicontractive Mappings Ştefan
More informationComputers and Mathematics with Applications
Computers and Mathematics with Applications 64 (2012) 643 650 Contents lists available at SciVerse ScienceDirect Computers and Mathematics with Applications journal homepage: www.elsevier.com/locate/camwa
More informationNew Iterative Algorithm for Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 20, 995-1003 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4392 New Iterative Algorithm for Variational Inequality Problem and Fixed
More informationScalar Asymptotic Contractivity and Fixed Points for Nonexpansive Mappings on Unbounded Sets
Scalar Asymptotic Contractivity and Fixed Points for Nonexpansive Mappings on Unbounded Sets George Isac Department of Mathematics Royal Military College of Canada, STN Forces Kingston, Ontario, Canada
More informationKrasnoselskii type algorithm for zeros of strongly monotone Lipschitz maps in classical banach spaces
DOI 10.1186/s40064-015-1044-1 RESEARCH Krasnoselskii type algorithm for zeros of strongly monotone Lipschitz maps in classical banach spaces Open Access C E Chidume 1*, A U Bello 1, and B Usman 1 *Correspondence:
More informationResearch Article Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions
Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 008, Article ID 84607, 9 pages doi:10.1155/008/84607 Research Article Generalized Mann Iterations for Approximating Fixed Points
More informationA generalized forward-backward method for solving split equality quasi inclusion problems in Banach spaces
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 4890 4900 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa A generalized forward-backward
More informationOn the simplest expression of the perturbed Moore Penrose metric generalized inverse
Annals of the University of Bucharest (mathematical series) 4 (LXII) (2013), 433 446 On the simplest expression of the perturbed Moore Penrose metric generalized inverse Jianbing Cao and Yifeng Xue Communicated
More informationViscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 016, 4478 4488 Research Article Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mappings in Hilbert
More informationSTRONG CONVERGENCE THEOREMS FOR COMMUTATIVE FAMILIES OF LINEAR CONTRACTIVE OPERATORS IN BANACH SPACES
STRONG CONVERGENCE THEOREMS FOR COMMUTATIVE FAMILIES OF LINEAR CONTRACTIVE OPERATORS IN BANACH SPACES WATARU TAKAHASHI, NGAI-CHING WONG, AND JEN-CHIH YAO Abstract. In this paper, we study nonlinear analytic
More informationAcademic Editor: Hari M. Srivastava Received: 29 September 2016; Accepted: 6 February 2017; Published: 11 February 2017
mathematics Article The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces Ali Abkar,
More information