COMMON FIXED POINT THEOREMS FOR MULTIVALUED OPERATORS ON COMPLETE METRIC SPACES
|
|
- Thomas Spencer
- 5 years ago
- Views:
Transcription
1 STUDIA UNIV. BABEŞ BOLYAI MATHEMATICA Volume XLVII Number 1 March 00 COMMON FIXED POINT THEOREMS FOR MULTIVALUED OPERATORS ON COMPLETE METRIC SPACES 1. Introduction The purpose of this paper is to prove a common fixed point theorem for multivalued operators defined on a complete metric space. Then as consequences we obtain some generalizations of several results proved in [6] for singlevalued operators. For other results of this type see [1] [] [3] and [5]. The metric conditions which appears in Theorem 3.1 generalize some conditions given in [6].. Preliminaries Let X be a nonempty set. We denote: P X := {A X A } and P cl X := {A P X A = Ā}. If X d is a metric space B P X and a A then Da B := inf{da b b B}. Definition.1. If T : X X is a multivalued operator then an element x X is a fixed point of T iff x T x. We denote by F T := {x X x T x} the fixed points set of T. Definition.. Let T n n N be a sequence of multivalued operators T n : X P X n N. Then we denote by ComT := {x X x T n x n N } = the common fixed points set of the sequence T n n N. n N F Tn 000 Mathematics Subject Classification. 7H10 5H5. Key words and phrases. fixed point multivalued operator common fixed point. 73
2 Lemma.3. I.A.Rus []. Let ϕ : R k + R + k N be a function and denote by ψ : R + R + the mapping given by ψt = ϕt t... t t R +. Suppose that the following conditions are satisfied: i r s r s R k + ϕr ϕs; ii ϕ is upper semi-continuous; iii ψt < t for each t > 0. Then lim ψn t = 0 for each t 0. In [6] T.Veerapandi and S.A.Kumar gave the following result: Theorem.. Let X be a Hilbert space Y P cl X and T n : Y Y for n N be a sequence of mappings. We suppose that at least one of the following conditions is satisfied: i there exist real numbers a b c satisfying 0 a b c < 1 and a + b + c < 1 such that for each x y Y and x y T i x T j y a x y + b x T i x + y T j y + + c x T j y + y T i x for i j; ii there exist a real number h satisfying 0 h < 1 such that for all x y Y and x y T i x T j y h max { x y 1 x T i x + y T j y } 1 x T j y + y T i x for i j. Then T n n N has a unique common fixed point. 3. The main results The first result of this section improve and generalize Theorem. in the multivoque case. Theorem 3.1. Let X d be a complete metric space and S T : X P cl X multivalued operators. We suppose that there exists a function ϕ : R 3 + R + such that: i r s r s R 3 + ϕr ϕs; ii ϕt t t < t for each t > 0; 7
3 COMMON FIXED POINT THEOREMS so that we have iii ϕ is continuous; iv for each x X any u x Sx and for all y X there exists u y T y d u x u y ϕ such that d x y d x u x + d y u y In these conditions F S = F T = {x }. d x u y + d y u x. Proof. Let x 0 X arbitrarily. Then we can construct a sequence x n X x n+1 Sx n x n+ T x n+1 Denote by d n := dx n x n+1 n N. n N. We have several steps in our proof. Step I. Let us prove that the sequence d n is monotone decreasing. Indeed we have successively: d n+1 = d x n+1 x n+ ϕ d x n x n+1 d x n x n+1 + d x n+1 x n+ d x n x n+ + d x n+1 x n+1 { < max d n ϕ d n d n + d n+1 d n + d n+1 d n + d n+1 } = d n from where it follows d n+1 < d n. By an analogous method we have d n+ < d n+1. Step II. We prove that lim d n = 0. For this purpose let us define ψ : R + R + by ψt = ϕt t t. Obviously ψ is monotone increasing and ψt < t t > 0. By induction we can prove that d n ψ n d 0 n 1. Indeed we have d 1 ϕ d 0 d 1 + d 0 d 0 + d 1 ϕd 0 d 0 d 0 = ψd 0. If inequality d n ψ n d 0 is true then we get successively: d n+1 ϕ d n d n + d n+1 d n + d n+1 ϕd n d n d n = ψd n ψψ n d 0 = ψ n+1 d 0. By passing to limit as n if d 0 > 0 it follows lim d n lim ψn d 0 = 0 and hence lim d n = 0. 75
4 lim d n = 0. For d 0 = 0 the sequence d n being decreasing it is obviously that Step III. We ll prove that the sequence x n is Cauchy in X i.e. for each ε > 0 there exists k N such that for each m n k dx m x n < ε. Suppose by contradiction that x n is not Cauchy sequence. Then there exists ε > 0 such that for each k N there exist m k n k N m k > n k k with the property dx mk x nk > ε. In what follows let us suppose the numbers mk and nk as follows: mk := inf{m k N m k > n k k dx nk x mk ε dx nk x mk > ε} and nk := n k. Then k N we have: ε < dx nk x mk dx nk x mk + dx mk x mk 1 + and Using step II we deduce that +dx mk 1 x mk. From the triangle inquality we get: lim dx nk x mk = ε. 1 k dx nk x mk 1 dx nk x mk dx mk 1 x mk dx nk+1 x mk 1 dx nk x mk dx mk 1 x mk + dx nk x nk+1. Using again step III and the relation 1 it follows lim dx nk x mk 1 = ε k Then we have successively: lim dx nk+1 x mk 1 = ε. k 76 dx nk x mk dx nk x nk+1 + dx nk+1 x mk dx nk x nk [ ϕd x nk x mk 1 d x nk x nk+1 + d x mk 1 x mk
5 COMMON FIXED POINT THEOREMS d x nk x mk + d x mk 1 x nk+1 ] 1. Because ϕ is continuous passing to the limit as k we have: ε [ ϕ ε 0 ε Step IV. We prove that F T. ] 1 [ ψε ] 1 < ε a contradiction. Because x n is Cauchy sequence in the complete metric space X d we obtain that there exists x X such that lim x n = x. From x n+1 Sx n we have that there exists u n T x such that: d x n+1 u n ϕ d x n x d x n x n+1 + d x u n d x n u n + d x x n+1 { < max d x n x d x n x n+1 + d x u n d x n u n + d x x n+1 from where i.e. := M. Consequently we have the following situations: a. Case M = d x n x. In this case we have d x n+1 u n d x n x lim dx n+1 u n lim dx n x = 0 lim dx n+1 u n = 0. < b. Case M = d x n x n+1 + d x u n. We deduce successively: d x n+1 u n d x n x n+1 + d x u n d x n x n+1 + [dx x n+1 + dx n+1 u n ] i.e. d x n+1 u n dx x n+1 dx n+1 u n [d x n x n+1 +d x x n+1 ] 0 therefore dx n+1 u n dx x n+1 + d x x n+1 + d x n x n+1. } 77
6 c. Case M = d x n u n + d x x n+1. In this case from the inequal- ity we have again Passing to the limit in this inequality as n we obtain lim dx n+1 u n = 0. d x n+1 u n d x n u n + d x x n+1 lim dx n+1 u n = 0. Passing to the limit as n in inequality dx u n dx x n+1 + dx n+1 u n on the basis of the limit lim dx n+1 u n = 0 we obtain dx u n 0 as n 0. Since u n T x n N and T x is a closed set it follows that x T x i.e. x F T. Step V. that F S F T. that We ll obtain now the conclusion of our theorem. We first prove Let x F S. From x Sx we have that there exists u T x d x u ϕ d x x d x x + d x u d x u + d x x. If we suppose that dx u > 0 then we obtain d x d x u d x u u ϕ 0 < d x u such a contradiction. Thus dx u = 0 which means that u = x. It follows that x T x and so F S F T. and T. we have 78 We shall prove now the equality F S = F T betwen the fixed points set for S If we assume that there exists y F T such that y x F S then d x y ϕ d x y = ϕ d x y 0 d x y + d y x = d x x + d y y d x y ψd x y < d x y
7 COMMON FIXED POINT THEOREMS a contradiction proving the fact that F S = F T P X. In fact we have obtained even more namely that F S = F T = {x }. Corollary 3.. Let X d be a complete metric space and S T : X P cl X multivalued operators. We suppose that there exist a b c R + a + b + c < 1 such that for each x X each u x Sx and for all y X have there exists u y T y so that we d u x u y a d x y + b [d x u x + d y u y ] + c [d x u y + d y u x ]. Then F S = F T = {x }. Proof. Applying Theorem 3.1 for the function ϕ : R 3 + R + ϕt 1 t t 3 = at 1 + bt + ct 3 which satisfies the conditions i ii and iii of this theorem we obtain the conclusion. Remark 3.3. If T and S are singlevalued operators then Corollary 3. is Theorem 3 from [6]. Corollary 3.. Let X d be a complete metric space and P cl X multivalued operators. We suppose that there exists h ]0 1[ S T : X such that for each x X any u x Sx and for all y X there exists u y T y so that we have { d u x u y h max d x y d x u x + d y u y In these conditions F S = F T = {x }. d x u y + d y u x Proof. We apply Theorem 3.1 for the function ϕ : R 3 + R + ϕt 1 t t 3 = h max{t 1 t t 3 } which satisfies the conditions i ii and iii of this theorem. Remark 3.5. Corollary 3. is a generalization for multivalued operators of Theorem from [6] theorem proved for singlevalued operators in Hilbert spaces. Remark 3.6. Let X d be a complete metric space and T n n N be a sequence of multivalued operators T n : X P cl X n N. If each pair of multivalued operators T 0 T n for n N satisfies similar conditions as in Theorem 3.1 then F Tn = F T0 = {x } for all n N. We next give a generalization of Theorem 1 of N.Negoescu []. }. 79
8 Theorem 3.7. Let X d be a compact metric space S T : X P cl X and ϕ : R 3 + R +. Suppose that the following conditions are satisfies: i r s; r s R 3 + ϕr ϕs; ii ϕt t t < t t > 0; iii iv S or T be continuous; d u x u y < ϕ d x y dx u x dy u y dx u y dy u x for all x y X x y and for all u x u y Sx T x. fixed point. In these conditions: a. S or T has a strict fixed point; b. if both S and T have such fixed points then the pair S T has a common Proof. a. Let S be continuous and we consider the function fx := Dx Sx. Because f is continuous on X it follows that f takes its minimum value i.e. there exists x 0 X such that fx 0 = inf{fx x X}. point of T. We prove that x 0 is a fixed point of S or some x 1 Sx 0 is a fixed Indeed we choose: x 1 Sx 0 be such that dx 0 x 1 = Dx 0 Sx 0 ; x T x 1 be such that dx 1 x = Dx 1 T x 1 ; x 3 Sx be such that dx x 3 = Dx Sx. We shall prove that Dx 0 Sx 0 = 0 or Dx 1 T x 1 = 0 i.e. x 0 Sx 0 or x 1 T x 1. We suppose that Dx 0 Sx 0 > 0 and Dx 1 T x 1 > 0. Hence using the inequality iv we have: d x 1 x < ϕ d x 0 x 1 dx 0 x 1 dx 1 x dx 0 x dx 1 x 1 { } max d x 0 x 1 dx 0 x 1 dx 1 x := M. Consequently we distinguish the following situations: I. Case M = d x 0 x 1. In this case we deduce dx 1 x < dx 0 x 1. II. Case M = dx 0 x 1 dx 1 x. In this case we have d x 1 x < dx 0 x 1 dx 1 x. Since dx 1 x = Dx 1 T x 1 > 0 it follows that dx 1 x < 80
9 COMMON FIXED POINT THEOREMS dx 0 x 1. Now d x 3 x < ϕ d x x 1 dx x 3 dx 1 x dx x dx 1 x 3 { } max d x 1 x dx x 3 dx 1 x. Analogously it follows that d x x 3 < d x 1 x or d x x 3 < dx x 3 dx 1 x. In the second situations if dx x 3 = 0 we obtain a contradiction. Thus it follows that dx x 3 < dx 1 x. Similarly we deduce successively: Dx Sx = dx x 3 < dx 1 x < dx 0 x 1 = fx 0 which contradict the minimality of fx 0. Therefore Dx 0 Sx 0 = 0 or Dx 1 T x 1 = 0. So x 0 Sx 0 or x 1 T x 1. b. We assume that there exist u Su and v T v such that u v. Then using the hypothesis iv we get again a contradiction: d u v < ϕ d u v du u dv v d u v d u v. So u=v meaning that u is a common fixed point of S and T. Remark 3.8. If ϕ : R 3 + R + ϕt 1 t t 3 = max{t 1 t t 3 } from Theorem 3.7 we get a result of Negoescu [ Theorem 1]. References Remark 3.9. We note that Theorem 3.7 is true for S = T : X P cl X. [1] I. Kubiaczyk Fixed points for contractive correspondences Demonstratio Math [] N. Negoescu Observations sur des paires d applications multivoques d un certain type de contractivité Bul. Instit. Politehnic Iaşi fasc [3] V. Popa Common fixed points of sequence of multifunctions Babes-Bolyai Univ. Seminar on Fixed Point Theory Preprint nr [] I.A. Rus Generalized contractions Babes-Bolyai Univ Seminar on Fixed Point Theory Preprint nr [5] I.A. Rus A. Petruşel A. Sîntămărian Data dependence of the fixed points set of c- multivalued weakly Picard operators Mathematica Cluj-Napoca to appear. [6] T. Veerapandi S.A. Kumar Common fixed point theorems of a sequence of mappings in Hilbert space Bull. Cal. Math. Soc Carol I High School Sibiu 00 Sibiu ROMANIA address: aurelmuntean@yahoo.com 81
10 Received:
Seminar on Fixed Point Theory Cluj-Napoca, Volume 1, 2000, nodeacj/journal.htm
Seminar on Fixed Point Theory Cluj-Napoca, Volume 1, 2000, 63-68 http://www.math.ubbcluj.ro/ nodeacj/journal.htm FIXED POINT THEOREMS FOR MULTIVALUED EXPANSIVE OPERATORS Aurel Muntean Carol I High School
More informationA NOTE ON MULTIVALUED MEIR-KEELER TYPE OPERATORS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LI, Number 4, December 2006 A NOTE ON MULTIVALUED MEIR-KEELER TYPE OPERATORS ADRIAN PETRUŞEL AND GABRIELA PETRUŞEL Dedicated to Professor Gheorghe Coman at
More informationBest proximity problems for Ćirić type multivalued operators satisfying a cyclic condition
Stud. Univ. Babeş-Bolyai Math. 62(207), No. 3, 395 405 DOI: 0.2493/subbmath.207.3. Best proximity problems for Ćirić type multivalued operators satisfying a cyclic condition Adrian Magdaş Abstract. The
More informationExistence and data dependence for multivalued weakly Ćirić-contractive operators
Acta Univ. Sapientiae, Mathematica, 1, 2 (2009) 151 159 Existence and data dependence for multivalued weakly Ćirić-contractive operators Liliana Guran Babeş-Bolyai University, Department of Applied Mathematics,
More informationFixed point theorems for Ćirić type generalized contractions defined on cyclic representations
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 8 (2015), 1257 1264 Research Article Fixed point theorems for Ćirić type generalized contractions defined on cyclic representations Adrian Magdaş
More informationFIXED POINT THEORY FOR MULTIVALUED OPERATORS ON A SET WITH TWO METRICS
Fixed Point Theory, Volume 8, No. 1, 2007, 97-104 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html FIXED POINT THEORY FOR MULTIVALUED OPERATORS ON A SET WITH TWO METRICS ADRIAN PETRUŞEL AND IOAN A. RUS
More informationCARISTI TYPE OPERATORS AND APPLICATIONS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVIII, Number 3, September 2003 Dedicated to Professor Gheorghe Micula at his 60 th anniversary 1. Introduction Caristi s fixed point theorem states that
More informationBest proximity points of Kannan type cyclic weak ϕ-contractions in ordered metric spaces
An. Şt. Univ. Ovidius Constanţa Vol. 20(3), 2012, 51 64 Best proximity points of Kannan type cyclic weak ϕ-contractions in ordered metric spaces Erdal Karapınar Abstract In this manuscript, the existence
More informationSOME RESULTS CONCERNING THE MULTIVALUED OPTIMIZATION AND THEIR APPLICATIONS
Seminar on Fixed Point Theory Cluj-Napoca, Volume 3, 2002, 271-276 http://www.math.ubbcluj.ro/ nodeacj/journal.htm SOME RESULTS CONCERNING THE MULTIVALUED OPTIMIZATION AND THEIR APPLICATIONS AUREL MUNTEAN
More informationON NADLER S MULTI-VALUED CONTRACTION PRINCIPLE IN COMPLETE METRIC SPACES
ISSN 2066-6594 Ann. Acad. Rom. Sci. Ser. Math. Appl. Vol. 10, No. 1/2018 ON NADLER S MULTI-VALUED CONTRACTION PRINCIPLE IN COMPLETE METRIC SPACES Adrian Petruşel Dedicated to Professor Mihail Megan on
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 informationCaristi-type Fixed Point Theorem of Set-Valued Maps in Metric Spaces
International Journal of Mathematical Analysis Vol. 11, 2017, no. 6, 267-275 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.717 Caristi-type Fixed Point Theorem of Set-Valued Maps in Metric
More informationFixed Points for Multivalued Mappings in b-metric Spaces
Applied Mathematical Sciences, Vol. 10, 2016, no. 59, 2927-2944 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.68225 Fixed Points for Multivalued Mappings in b-metric Spaces Seong-Hoon
More informationĆirić type fixed point theorems
Stud. Univ. Babeş-Bolyai Math. 59(2014), No. 2, 233 245 Ćirić type fixed point theorems Adrian Petruşel Abstract. The purpose of this paper is to review some fixed point and strict fixed point results
More informationSPACES ENDOWED WITH A GRAPH AND APPLICATIONS. Mina Dinarvand. 1. Introduction
MATEMATIČKI VESNIK MATEMATIQKI VESNIK 69, 1 (2017), 23 38 March 2017 research paper originalni nauqni rad FIXED POINT RESULTS FOR (ϕ, ψ)-contractions IN METRIC SPACES ENDOWED WITH A GRAPH AND APPLICATIONS
More informationPerov s fixed point theorem for multivalued mappings in generalized Kasahara spaces
Stud. Univ. Babeş-Bolyai Math. 56(2011), No. 3, 19 28 Perov s fixed point theorem for multivalued mappings in generalized Kasahara spaces Alexandru-Darius Filip Abstract. In this paper we give some corresponding
More informationFixed Point Problems for α-ψ-weakly Contractive Operators on KST Spaces
Filomat 31:14 (017), 4441 4454 https://doi.org/10.98/fil1714441g Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Point Problems
More informationA fixed point theorem for (µ, ψ)-generalized f-weakly contractive mappings in partially ordered 2-metric spaces
Mathematica Moravica Vol. 21, No. 1 (2017), 37 50 A fixed point theorem for (µ, ψ)-generalized f-weakly contractive mappings in partially ordered 2-metric spaces Nguyen Trung Hieu and Huynh Ngoc Cam Abstract.
More informationFixed point of ϕ-contraction in metric spaces endowed with a graph
Annals of the University of Craiova, Mathematics and Computer Science Series Volume 374, 2010, Pages 85 92 ISSN: 1223-6934 Fixed point of ϕ-contraction in metric spaces endowed with a graph Florin Bojor
More informationFIXED POINTS AND CONTINUITY OF ALMOST CONTRACTIONS
FIXED POINTS AND CONTINUITY OF ALMOST CONTRACTIONS VASILE BERINDE AND MĂDĂLINA PĂCURAR Abstract. Almost contractions form a class of generalized contractions that includes several contractive type mappings
More informationCommon fixed points for α-ψ-ϕ-contractions in generalized metric spaces
Nonlinear Analysis: Modelling and Control, 214, Vol. 19, No. 1, 43 54 43 Common fixed points for α-ψ-ϕ-contractions in generalized metric spaces Vincenzo La Rosa, Pasquale Vetro Università degli Studi
More informationMohamed Akkouchi WELL-POSEDNESS OF THE FIXED POINT. 1. Introduction
F A S C I C U L I M A T H E M A T I C I Nr 45 2010 Mohamed Akkouchi WELL-POSEDNESS OF THE FIXED POINT PROBLEM FOR φ-max-contractions Abstract. We study the well-posedness of the fixed point problem for
More informationFIXED POINTS AND CYCLIC CONTRACTION MAPPINGS UNDER IMPLICIT RELATIONS AND APPLICATIONS TO INTEGRAL EQUATIONS
SARAJEVO JOURNAL OF MATHEMATICS Vol.1 (23) (214), 257 27 DOI: 1.5644/SJM.1.2.11 FIXED POINTS AND CYCLIC CONTRACTION MAPPINGS UNDER IMPLICIT RELATIONS AND APPLICATIONS TO INTEGRAL EQUATIONS HEMANT KUMAR
More informationSome Fixed Point Theorems for Certain Contractive Mappings in G-Metric Spaces
Mathematica Moravica Vol. 17-1 (013) 5 37 Some Fixed Point Theorems for Certain Contractive Mappings in G-Metric Spaces Amit Singh B. Fisher and R.C. Dimri Abstract. In this paper we prove some fixed point
More informationSome Fixed Point Results for (α, β)-(ψ, φ)-contractive Mappings
Filomat 28:3 214), 635 647 DOI 12298/FIL143635A Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://wwwpmfniacrs/filomat Some Fixed Point Results for α, β)-ψ,
More informationFIXED POINT THEOREMS FOR NONSELF SINGLE-VALUED ALMOST CONTRACTIONS
Fixed Point Theory, 14(2013), No. 2, 301-312 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html FIXED POINT THEOREMS FOR NONSELF SINGLE-VALUED ALMOST CONTRACTIONS VASILE BERINDE AND MĂDĂLINA PĂCURAR Department
More informationNOTE ON A FIXED POINT THEOREM
Fixed Point Theory, Volume 5, No. 1, 2004, 81-85 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.htm NOTE ON A FIXED POINT THEOREM DOREL MIHEŢ West University of Timişoara Faculty of Mathematics Bv. V. Parvan
More informationCommon fixed points of generalized contractive multivalued mappings in cone metric spaces
MATHEMATICAL COMMUNICATIONS 365 Math. Commun., Vol. 14, No., pp. 365-378 (009) Common fixed points of generalized contractive multivalued mappings in cone metric spaces Mujahid Abbas 1,, B. E. Rhoades
More informationFIXED POINT THEOREMS IN D-METRIC SPACE THROUGH SEMI-COMPATIBILITY. 1. Introduction. Novi Sad J. Math. Vol. 36, No. 1, 2006, 11-19
Novi Sad J Math Vol 36, No 1, 2006, 11-19 FIXED POINT THEOREMS IN D-METRIC SPACE THROUGH SEMI-COMPATIBILITY Bijendra Singh 1, Shobha Jain 2, Shishir Jain 3 Abstract The objective of this paper is to introduce
More informationA NEW PERSPECTIVE FOR MULTIVALUED WEAKLY PICARD OPERATORS. Gonca Durmaz and Ishak Altun
PUBLICATIONS DE L INSTITUT MATHÉMATIQUE Nouvelle série, tome 101(115) (2017), 197 204 https://doi.org/10.2298/pim1715197d A NEW PERSPECTIVE FOR MULTIVALUED WEAKLY PICARD OPERATORS Gonca Durmaz and Ishak
More informationCommon Fixed Point Theorems for Ćirić-Berinde Type Hybrid Contractions
International Journal of Mathematical Analysis Vol. 9, 2015, no. 31, 1545-1561 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.54125 Common Fixed Point Theorems for Ćirić-Berinde Type
More informationFixed Point Theorem for Cyclic (µ, ψ, φ)-weakly Contractions via a New Function
DOI: 10.1515/awutm-2017-0011 Analele Universităţii de Vest, Timişoara Seria Matematică Informatică LV, 2, 2017), 3 15 Fixed Point Theorem for Cyclic µ, ψ, φ)-weakly Contractions via a New Function Muaadh
More informationAPPROXIMATE FIXED POINT OF REICH OPERATOR. 1. Introduction
APPROXIMATE FIXED POINT OF REICH OPERATOR D. DEY and M. SAHA Abstract. In the present paper, we study the existence of approximate fixed point for Reich operator together with the property that the ε-fixed
More informationFIXED POINT THEOREMS OF KRASNOSELSKII TYPE IN A SPACE OF CONTINUOUS FUNCTIONS
Fixed Point Theory, Volume 5, No. 2, 24, 181-195 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.htm FIXED POINT THEOREMS OF KRASNOSELSKII TYPE IN A SPACE OF CONTINUOUS FUNCTIONS CEZAR AVRAMESCU 1 AND CRISTIAN
More informationBEST APPROXIMATIONS AND ORTHOGONALITIES IN 2k-INNER PRODUCT SPACES. Seong Sik Kim* and Mircea Crâşmăreanu. 1. Introduction
Bull Korean Math Soc 43 (2006), No 2, pp 377 387 BEST APPROXIMATIONS AND ORTHOGONALITIES IN -INNER PRODUCT SPACES Seong Sik Kim* and Mircea Crâşmăreanu Abstract In this paper, some characterizations of
More informationFixed point theorems for Zamfirescu mappings in metric spaces endowed with a graph
CARPATHIAN J. MATH. 31 2015, No. 3, 297-305 Online version availale at http://carpathian.um.ro Print Edition: ISSN 1584-2851 Online Edition: ISSN 1843-4401 Fixed point theorems for Zamfirescu mappings
More informationCommon fixed point of -approximative multivalued mapping in partially ordered metric space
Filomat 7:7 (013), 1173 118 DOI 1098/FIL1307173A Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://wwwpmfniacrs/filomat Common fixed point of -approximative
More informationBEST PROXIMITY POINT RESULTS VIA SIMULATION FUNCTIONS IN METRIC-LIKE SPACES
Kragujevac Journal of Mathematics Volume 44(3) (2020), Pages 401 413. BEST PROXIMITY POINT RESULTS VIA SIMULATION FUNCTIONS IN METRIC-LIKE SPACES G. V. V. J. RAO 1, H. K. NASHINE 2, AND Z. KADELBURG 3
More informationFixed Points Results via Simulation Functions
Filomat 30:8 (2016), 2343 2350 DOI 10.2298/FIL1608343K Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Points Results via
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 informationCommon fixed point of multivalued graph contraction in metric spaces
Int. J. Nonlinear Anal. Appl. 7 (2016) No. 1, 225-230 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2015.309 Common fixed point of multivalued graph contraction in metric spaces Masoud
More informationA fixed point theorem for weakly Zamfirescu mappings
A fixed point theorem for weakly Zamfirescu mappings David Ariza-Ruiz Dept. Análisis Matemático, Fac. Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain Antonio Jiménez-Melado Dept.
More informationBest proximity points for generalized α η ψ-geraghty proximal contraction mappings
Mathematica Moravica Vol. 1, No. (017), 85 10 Best proximity points for generalized α η ψ-geraghty proximal contraction mappings K.K.M. Sarma and Yohannes Gebru Abstract. In this paper, we introduce the
More informationNew extension of some fixed point results in complete metric spaces
DOI 10.1515/tmj-017-0037 New extension of some fixed point results in complete metric spaces Pradip Debnath 1,, Murchana Neog and Stojan Radenović 3 1, Department of Mathematics, North Eastern Regional
More informationFIXED POINT THEOREMS AND CHARACTERIZATIONS OF METRIC COMPLETENESS. Tomonari Suzuki Wataru Takahashi. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 8, 1996, 371 382 FIXED POINT THEOREMS AND CHARACTERIZATIONS OF METRIC COMPLETENESS Tomonari Suzuki Wataru Takahashi
More informationCOMMON FIXED POINT THEOREMS OF CARISTI TYPE MAPPINGS WITH w-distance. Received April 10, 2010; revised April 28, 2010
Scientiae Mathematicae Japonicae Online, e-2010, 353 360 353 COMMON FIXED POINT THEOREMS OF CARISTI TYPE MAPPINGS WITH w-distance Tomoaki Obama Daishi Kuroiwa Received April 10, 2010; revised April 28,
More informationBest proximity point results in set-valued analysis
Nonlinear Analysis: Modelling and Control, Vol. 21, No. 3, 293 305 ISSN 1392-5113 http://dx.doi.org/10.15388/na.2016.3.1 Best proximity point results in set-valued analysis Binayak S. Choudhury a, Pranati
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 informationA GENERALIZATION OF CONTRACTION PRINCIPLE IN QUASI-METRIC SPACES
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 9 Issue 1(2017), Pages 92-108. A GENERALIZATION OF CONTRACTION PRINCIPLE IN QUASI-METRIC SPACES HAMZA
More informationA Common Fixed Point Theorem for Multivalued Mappings Through T-weak Commutativity
Mathematica Moravica Vol. 10 (2006), 55 60 A Common Fixed Point Theorem for Multivalued Mappings Through T-weak Commutativity I. Kubiaczyk and Bhavana Deshpande Abstract. In this paper, we prove a common
More informationUsing Implicit Relations to Prove Unified Fixed Point Theorems in Metric and 2-Metric Spaces
BULLETIN of the Malaysian Mathematical Sciences Society http://math.usm.my/bulletin Bull. Malays. Math. Sci. Soc. (2) 33(1) (2010), 105 120 Using Implicit Relations to Prove Unified Fixed Point Theorems
More informationFIXED POINTS FOR MULTIVALUED CONTRACTIONS WITH RESPECT TO A w-distance.
Scientiae Mathematicae Japonicae Online, e-2009, 611 619 611 FIXED POINTS FOR MULTIVALUED CONTRACTIONS WITH RESPECT TO A w-distance. Received April 22, 2008; Revised November 9, 2009 Abstract. The aim
More informationCOMMON FIXED POINT THEOREMS FOR FOUR MAPPINGS WITH SOME WEAK CONDITIONS OF COMMUTATIVITY
Novi Sad J. Math. Vol. 36, No. 1, 006, 75-86 COMMON FIXED POINT THEOREMS FOR FOUR MAPPINGS WITH SOME WEAK CONDITIONS OF COMMUTATIVITY Duran Turkoglu 1, Ishak Altun 1, Brian Fisher Abstract. Some results
More informationFixed Point Theorem for Cyclic Maps on Partial Metric spaces
Appl. Math. Inf. Sci. 6, No. 1, 39-44 (01) 39 Applied Mathematics & Information Sciences An International Journal Fixed Point Theorem for Cyclic Maps on Partial Metric spaces E. Karapınar 1, İ. M. Erhan
More informationCiric-type δ-contractions in metric spaces endowedwithagraph
Chifu and Petruşel Journal of Inequalities and Applications 2014, 2014:77 R E S E A R C H Open Access Ciric-type δ-contractions in metric spaces endowedwithagraph Cristian Chifu 1* and Adrian Petruşel
More informationEXISTENCE OF STRONG SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS
EXISTENCE OF STRONG SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS Adriana Buică Department of Applied Mathematics Babeş-Bolyai University of Cluj-Napoca, 1 Kogalniceanu str., RO-3400 Romania abuica@math.ubbcluj.ro
More informationKannan mappings vs. Caristi mappings: An easy example
Kannan mappings vs. Caristi mappings: An easy example Carmen Alegre, S. R. WATS 2016, Valencia June 22, 2016 1 / 13 In 1922, Banach published his famous fixed point theorem wich is stated as follows. Theorem
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 informationGoebel and Kirk fixed point theorem for multivalued asymptotically nonexpansive mappings
CARPATHIAN J. MATH. 33 (2017), No. 3, 335-342 Online version at http://carpathian.ubm.ro Print Edition: ISSN 1584-2851 Online Edition: ISSN 1843-4401 Goebel and Kirk fixed point theorem for multivalued
More informationON RANDOM FIXED POINTS IN RANDOM CONVEX STRUCTURES
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LIII, Number 2, June 2008 ON RANDOM FIXED POINTS IN RANDOM CONVEX STRUCTURES ASHOK GANGULY, RAGHVENDRA SINGH CHANDEL, AND RAVINDRA PARSAI Abstract. In this
More informationCOUPLED FIXED AND COINCIDENCE POINT THEOREMS FOR GENERALIZED CONTRACTIONS IN METRIC SPACES WITH A PARTIAL ORDER
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS N. 39 2018 (434 450) 434 COUPLED FIXED AND COINCIDENCE POINT THEOREMS FOR GENERALIZED CONTRACTIONS IN METRIC SPACES WITH A PARTIAL ORDER K. Ravibabu Department
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 informationEcon Lecture 3. Outline. 1. Metric Spaces and Normed Spaces 2. Convergence of Sequences in Metric Spaces 3. Sequences in R and R n
Econ 204 2011 Lecture 3 Outline 1. Metric Spaces and Normed Spaces 2. Convergence of Sequences in Metric Spaces 3. Sequences in R and R n 1 Metric Spaces and Metrics Generalize distance and length notions
More informationPATA TYPE FIXED POINT THEOREMS OF MULTIVALUED OPERATORS IN ORDERED METRIC SPACES WITH APPLICATIONS TO HYPERBOLIC DIFFERENTIAL INCLUSIONS
U.P.B. Sci. Bull., Series A, Vol. 78, Iss. 4, 216 ISSN 1223-727 PATA TYPE FIXED POINT THEOREMS OF MULTIVALUED OPERATORS IN ORDERED METRIC SPACES WITH APPLICATIONS TO HYPERBOLIC DIFFERENTIAL INCLUSIONS
More informationABSTRACT AND CONCRETE GRONWALL LEMMAS
Fixed Point Theory, 1(29), No. 2, 221-228 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html ABSTRACT AND CONCRETE GRONWALL LEMMAS CECILIA CRĂCIUN AND NICOLAE LUNGU Colfe s School Horn Park Lane London, SE12
More informationRelevant Classes of Weakly Picard Operators
DOI: 10.1515/awutm -2016-0019 Analele Universităţii de Vest, Timişoara Seria Matematică Informatică LIV, 2, (2016), 131 147 Relevant Classes of Weakly Picard Operators Ioan A. Rus Abstract. In this paper
More informationFIXED POINTS OF MULTIVALUED MAPPING SATISFYING CIRIC TYPE CONTRACTIVE CONDITIONS IN G-METRIC SPACES
Hacettepe Journal of Mathematics and Statistics Volume 4() (03), 9 FIXED POINTS OF MULTIVALUED MAPPING SATISFYING CIRIC TYPE CONTRACTIVE CONDITIONS IN G-METRIC SPACES Mujahid Abbas, Talat Nazır and B.
More informationCommon Fixed Point Results in S-metric Spaces
Journal of Advances in Applied Mathematics, Vol. 4, No. 2, April 2019 https://dx.doi.org/10.22606/jaam.2019.42002 45 Common Fixed Point Results in S-metric Spaces Jierong Yao * and Liping Yang School of
More informationOccasionally Weakly Compatible Mapping in Cone Metric Space
Applied Mathematical Sciences, Vol. 6, 2012, no. 55, 2711-2717 Occasionally Weakly Compatible Mapping in Cone Metric Space Arvind Bhatt Applied Science Department (Mathematics) Bipin trpathi Kumaun institute
More informationFixed Point Theorems for -Monotone Maps on Partially Ordered S-Metric Spaces
Filomat 28:9 (2014), 1885 1898 DOI 10.2298/FIL1409885D Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Point Theorems for
More informationFIXED POINTS OF MULTIVALUED MAPPINGS IN CERTAIN CONVEX METRIC SPACES. Tomoo Shimizu Wataru Takahashi. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 8, 1996, 197 203 FIXED POINTS OF MULTIVALUED MAPPINGS IN CERTAIN CONVEX METRIC SPACES Tomoo Shimizu Wataru Takahashi
More informationA fixed point theorem for w-distance
A fixed point theorem for w-distance A. Razani, Z. Mazlumi Nezhad and M. Boujary Abstract. In this paper, a fixed point theorem for a (Φ, Ψ, p)-contractive map on a complete metric space is proved. In
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 informationA fixed point theorem for multivalued mappings
Electronic Journal of Qualitative Theory of Differential Equations 24, No. 17, 1-1; http://www.math.u-szeged.hu/ejqtde/ A fixed point theorem for multivalued mappings Cezar AVRAMESCU Abstract A generalization
More informationCondensing KKM maps and its applications. Ivan D. Arand - elović, Z.Mitrović
Condensing KKM maps and its applications Ivan D. Arand - elović, Z.Mitrović October 16, 2015 Zoran Mitrović and Ivan Arand - elović. Existence of Generalized Best Approximations, Journal of Nonlinear and
More informationCommon fixed points for a class of multi-valued mappings and application to functional equations arising in dynamic programming
Malaya J. Mat. 2(1)(2014) 82 90 Common fixed points for a class of multi-valued mappings and application to functional equations arising in dynamic programming A. Aghajani, a E. Pourhadi b, a,b School
More informationLuljeta Kikina, Kristaq Kikina A FIXED POINT THEOREM IN GENERALIZED METRIC SPACES
DEMONSTRATIO MATHEMATICA Vol. XLVI No 1 2013 Luljeta Kikina, Kristaq Kikina A FIXED POINT THEOREM IN GENERALIZED METRIC SPACES Abstract. A generalized metric space has been defined by Branciari as a metric
More information(ψ,φ,θ)-weak contraction of continuous and discontinuous functions
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 8 (2017), pp. 4135 4140 Research India Publications http://www.ripublication.com/gjpam.htm (ψ,φ,θ)-weak contraction of continuous
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 informationA Quadruple Fixed Point Theorem for Contractive Type Condition by Using ICS Mapping and Application to Integral Equation
Mathematica Moravica Vol. - () 3 A Quadruple Fixed Point Theorem for Contractive Type Condition by Using ICS Mapping and Application to Integral Equation K.P.R. Rao G.N.V. Kishore and K.V. Siva Parvathi
More informationA Fixed Point Theorem and its Application in Dynamic Programming
International Journal of Applied Mathematical Sciences. ISSN 0973-076 Vol.3 No. (2006), pp. -9 c GBS Publishers & Distributors (India) http://www.gbspublisher.com/ijams.htm A Fixed Point Theorem and its
More informationCoincidence point results of multivalued weak C-contractions on metric spaces with a partial order
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 6 (2013), 7 17 Research Article Coincidence point results of multivalued weak C-contractions on metric spaces with a partial order Binayak S. Choudhury
More informationCOMMON FIXED POINT THEOREM OF THREE MAPPINGS IN COMPLETE METRIC SPACE
COMMON FIXED POINT THEOREM OF THREE MAPPINGS IN COMPLETE METRIC SPACE Latpate V.V. and Dolhare U.P. ACS College Gangakhed DSM College Jintur Abstract:-In this paper we prove common fixed point theorem
More information1 Introduction and preliminaries
Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Filomat 5: (0), 5 3 DOI: 0.98/FIL05D MULTIVALUED GENERALIZATIONS OF THE KANNAN FIXED POINT THEOREM
More informationFIXED POINT AND COMMON FIXED POINT THEOREMS IN CONE BALL-METRIC SPACES. 1. Introduction and preliminaries
Asia Pacific Journal of Mathematics, Vol. 1, No. 1 (2014), 67-85 ISSN 2357-2205 FIXED POINT AND COMMON FIXED POINT THEOREMS IN CONE BALL-METRIC SPACES ANIMESH GUPTA Department of Applied Mathematics, Vidhyapeeth
More informationFIXED POINT THEOREM ON MULTI-VALUED MAPPINGS
International Journal of Analysis and Applications ISSN 2291-8639 Volume 1, Number 2 (2013), 123-127 http://www.etamaths.com FIXED POINT THEOREM ON MULTI-VALUED MAPPINGS J.MARIA JOSEPH 1,, E. RAMGANESH
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 informationSome Generalizations of Caristi s Fixed Point Theorem with Applications
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 12, 557-564 Some Generalizations of Caristi s Fixed Point Theorem with Applications Seong-Hoon Cho Department of Mathematics Hanseo University, Seosan
More informationSOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION. Ishak Altun and Duran Turkoglu
TAIWANESE JOURNAL O MATHEMATICS Vol. 13, No. 4, pp. 1291-134, August 29 This paper is available online at http://www.tjm.nsysu.edu.tw/ SOME IXED POINT THEOREMS OR WEAKLY COMPATIBLE MAPPINGS SATISYING AN
More informationWEAK SUB SEQUENTIAL CONTINUOUS MAPS IN NON ARCHIMEDEAN MENGER PM SPACE
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org /JOURNALS / BULLETIN Vol. 7(2017), 65-72 Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS
More informationPICARD OPERATORS IN b-metric SPACES VIA DIGRAPHS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 9 Issue 3(2017), Pages 42-51. PICARD OPERATORS IN b-metric SPACES VIA DIGRAPHS SUSHANTA KUMAR MOHANTA
More informationF -contractions of Hardy Rogers type and application to multistage decision processes
Nonlinear Analysis: Modelling and Control, Vol. 2, No. 4, 53 546 ISSN 392-53 http://dx.doi.org/0.5388/na.206.4.7 F -contractions of Hardy Rogers type and application to multistage decision processes Francesca
More informationNew Generalizations of Caristi s Fixed Point Theorem Via Brézis Browder Principle
Mathematica Moravica Vol. 8 1 (2004), 1 5 New Generalizations of Caristi s Fixed Point Theorem Via Brézis Browder Principle Temistocle Bîrsan Abstract. In this paper, some generalizations of Caristi s
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 informationSome new fixed point theorems in metric spaces
Mathematica Moravica Vol. 20:2 (206), 09 2 Some new fixed point theorems in metric spaces Tran Van An and Le Thanh Quan Abstract. In this paper, the main results of [3] are generalized. Also, examples
More informationIntegral type Fixed point Theorems for α-admissible Mappings Satisfying α-ψ-φ-contractive Inequality
Filomat 3:12 (216, 3227 3234 DOI 1.2298/FIL1612227B Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Integral type Fixed point Theorems
More informationWEAK SUB SEQUENTIAL CONTINUOUS MAPS IN NON ARCHIMEDEAN MENGER PM SPACE VIA C-CLASS FUNCTIONS
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org /JOURNALS / BULLETIN Vol. 8(2018), 135-143 DOI: 10.7251/BIMVI1801135A Former BULLETIN
More informationOn the Existence of Bounded Solutions to a Class of Nonlinear Initial Value Problems with Delay
Filomat : (27, 25 5 https://doi.org/.2298/fil725a Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat On the Existence of Bounded Solutions
More informationSOME FIXED POINT RESULTS FOR ADMISSIBLE GERAGHTY CONTRACTION TYPE MAPPINGS IN FUZZY METRIC SPACES
Iranian Journal of Fuzzy Systems Vol. 4, No. 3, 207 pp. 6-77 6 SOME FIXED POINT RESULTS FOR ADMISSIBLE GERAGHTY CONTRACTION TYPE MAPPINGS IN FUZZY METRIC SPACES M. DINARVAND Abstract. In this paper, we
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 information