Fixed Point Result in Probabilistic Space
|
|
- Delphia Williamson
- 5 years ago
- Views:
Transcription
1 International Mathematical Forum, 4, 2009, no. 43, Fixed Point Result in Probabilistic Space Vanita Ben Dhagat, Satyendra Nath and Nirmal Kumar Jai Narain college of Technology, Bairasia Road, Bhopal M.P., India Abstract In this paper we prove minimization theorem in the generating space of quasi probabilistic metric space. Also we prove common fixed point theorem for the space which satisfy the minimization theorem. Mathematics Subject Classification: 54H25, 47H0 Keywords: Generating space of quasi probabilistic metric family, quasi compatible mapping, Minimization theorem, common fixed point Introduction and Preliminaries Minimization theorem in generating space of quasi metric space was given in [4].Let X be a non empty set and {d α : α (0,]} be family of mapping d α from XxX into R +. {X, d α } is called generating space of metric family if it satisfy following axioms: (GM ) For any two distinct points x and y in X such that d α (x,y) 0, α (0,] (GM 2) - d α (x,y) = 0 if x=y and α (0,] (GM 3) - d α (x,y) = d α (y,x) For all x, y in X and α (0,] (GM 4) - For any α (0,] there exists α,α 2 (0,α] such that α +α 2 α and so d α (x,y) d α (x,z) + d α2 (z,y) (GM 5) - d α (x,y) is non increasing and left continuous in α and x,y,z in X. Throughout this paper, we assume that k:(0,] (0, ) is a non decreasing function satisfying the condition K = Sup k(α) α
2 238 V. Ben Dhagat, S. Nath and N. Kumar Probabilistic metric space was first introduced by Menger []. Later many authors Schweizer and Sklar [3] and Mishara [2] and others. Throughout this paper D is the set of all left continuous distribution functions. A function Δ:[0,]x[0,] D is called a t-norm if the following conditions are satisfied: (T-) Δ(a,b) = Δ(b,a), (T-2) Δ(a,) = a, (T-3) Δ(a,Δ(b,c)) = Δ(Δ(a,b),c), (T-4) Δ(a,b) Δ(c,d) for a c and b d. Definition. A triple (X,F,Δ) is called a Menger probabilistic metric space if X is a nonempty set, Δ is a t-norm and F:XxX D is a mapping satisfying the following conditions: (PM-) Fx,y(t) = for all t>0 if and only if x=y, (PM-2) Fx,y(0) = 0, (PM-3) Fx,y = Fy,x, (PM-4) Fx,y(s+t) Δ( Fx,y(s), Fx,y(t)) for all x,y,z X, s,t 0. Remark: If Δ satisfies the condition supδ(t,t) =, then there exists topology T on X such that (X,T ) is a Hausdorff topological space and the family of sets U(p) = {Up(ε,λ):ε>0,λ (0,]}, p X, is a basis of neighborhood of the point p for T, where Up(ε,λ) = { : Fx,p(ε) >-λ}. Usually, the topology T is called (ε,λ) topology on (X,F,Δ). Proposition : Let (X,F,Δ) be a Menger probabilistic metric space with the t-norm Δ satisfying the condition: supδ(t,t) =. () t> For any α (0,], we define d α :XxX R + as follows: d α (x,y) = inf { t>0: Fx,y(t) >-α} (2) Then (i) (X, d α : α (0,]) is a generating space of quasi metric family and (ii) the topology T(d α ) on (X, d α : α (0,]) coincide with the (ε,λ) topology T on (X,F,Δ). Proof : (i) From the definition of (d α : α (0,]), it is easy to see that d α : α (0,]) satisfies the condition (QM-) and (QM-2) in definition. Besides, it follows clearly that (d α ) is non-increasing in α. Next we prove that d α is left continuous in α. For any given α (0,] and ε>0, from definition d α, there exists a t >0 such that t < d α (x,y) + ε and Fx,y(t ) >-α. Letting δ = Fx,y(t ) - (-α ) >0 and λ (α -δ,α ], we have -α < -λ < -(α -δ) = Fx,y(t ), which implies that t {t>0: Fx,y(t) >-λ}. Hence we have d α (x,y) d λ (x,y) = inf {t>0: Fx,y(t) >-λ} t < d α (x,y)+ε, which shows that d α is left continuous in α.
3 Fixed point results in probabilistic space 239 Now, we prove that (X, d α : α (0,]) also satisfies the condition (QM-3). By the condition (), for any given α (0,], there exists an μ (0,α] such that Δ(-μ, -μ) > -α Letting d μ (x,z) = σ and d μ (z,y) = β, from (2), for any given ε>0, we have Fx,z (σ+ε) > -μ, Fz,y (β+ε) > -μ and so Fx,y (σ + β + 2ε) Δ( Fx,z (σ+ε),fz,y (β+ε)) Δ(-μ, -μ) > -α. Hence we have d α (x,y) (σ + β + 2ε) = d μ (x,z) + d μ (z,y) +2ε. d α (x,y) d μ (x,z) + d μ (z,y). (ii) to prove the condition, it is enough to prove that for any ε>0 and α (0,], d α (x,y) < ε if and only if Fx,y (ε) > -α. In fact if d α (x,y) < ε, from (2), we have Fx,y (ε-μ) > -α. Conversely, if Fx,y (ε) > -α, since Fx,y is a left continuous distribution function, there exists an μ > 0 such that Fx,y (ε-μ) > -α. Hence d α (x,y) ε-μ < ε. This complete the proof. Remark: Such Menger probabilistic metric space with (2) is called generating space of quasi probabilistic metric space. Definition : Let S and T be mappings from a generating space of quasi metric family (X, d α : α (0,]) into itself. The mappings S and T are said to be quasi compatible if d α (STx n, TSx n ) 0 as n for all α (0,]. Whenever {x n } is a sequence in X such that limsx n = lim Tx n = p, for some p in X. Theorem. Let (X,F,Δ ) and (X 2,F 2,Δ 2 ) be two complete generating space of quasi probabilistic metric space. with t-norm satisfying the condition (). Let f : X X 2 be a mapping, T:X X be a continuous mapping satisfying inf{t>0:f Tx,Ty (t) > -α} inf{t>0:/2(f x,ty (t)+ F Tx,y (t)) > -α} and inf{t>0:f 2 f (Tx), f (Ty) (t) > -α} inf{t>0:/2(f 2 x,ty (t)+ F 2 Tx,y (t))> -α} for all x,y in X and α (0,]. Let ψ: R R be a non decreasing continuous function, bounded from below and φ:f(x ) R a lower semi continuous function, bounded from below. Assume that for any p X with inf ψ(φ(f(x))) < ψ(φ(f(p))), there exists q X with p Tq and Max{/2[inf{t>0:(F q,tp (t)> -α}+ inf{t>0:(f p,tq (t)> -α}], c/2[[inf{t>0:(f 2 f (q),f (Tp) (t)> -α}+ inf{t>0:(f 2 f (p), f (Tq) (t)> -α}]} k(α) [ψ(φ(f(p))) - ψ(φ(f(q)))], where c >0 is a given constant. Then there exists x 0 in X, such that inf ψ(φ(f(x))) = ψ(φ(f(x 0 ))) Proof: Let us suppose inf ψ(φ(f(x))) = ψ(φ(f(y))) for every y X and chose p X
4 240 V. Ben Dhagat, S. Nath and N. Kumar with ψ(φ(f(p)))<. Then we define a sequence {p n } X with p = p. Suppose p n is known and consider Wn = {w X : max {/2[inf{t>0:(F w,tpn (t)> -α}+ inf{t>0:(f Tw,pn (t)> -α}], c/2[[inf{t>0:(f 2 f (w),f (T( p n )) (t)> -α}+ inf{t>0:(f 2 f (Tw), f( p n ) (t)> -α}]}..(4) k(α) [ψ(φ(f(p n ))) - ψ(φ(f(w)))] for any α (0,]. Since Wn is nonvoid set therefore there exists w Wn such that p n Tw. We can choose p n+ Wn such that p n Tp n+ and ψ(φ(f(p n+ ))) inf ψ(φ(f(x))) - /2 [[ψ(φ(f(p n ))) inf ψ(φ(f(x)))] (5) we observe that [ψ(φ(f(p n+ )))] is a non increasing lower bounded sequence, hence it is convergent sequence. Now we prove that {p n } and { f(p n )}are cauchy sequences, Max[inf{t>0:(F T( p n),t( p n +) (t)> -α}, c inf{t>0:(f 2 f (T( p n)), f (T( p n +)) (t)> -α}] max { /2[inf{t>0:(F p n,t( p n+) (t)> -α}+ inf{t>0:(f p n+,t( p n) (t)> -α}], c/2[[inf{t>0:(f 2 f ( p n ),f (T( p n+ )) (t)> -α}+ inf{t>0:(f 2 f (T( p n)), f( p n ) (t)> -α}]} k(α) [ψ(φ(f(p n ))) - ψ(φ(f(p n+ )))] Now for all n,m N, n< m there exists μ α, μ = μ(n,m) such that Max[inf{t>0:(F T( p n),t( p m) (t)> -α}, c inf{t>0:(f 2 f (T( p n)), f (T( p m)) (t)> -α}] m- Σ j = n max { /2[inf{t>0:(F p j,t( p j+) (t)> -μ}+ inf{t>0:(f p j+,t( p j) (t)> -μ}], c/2[[inf{t>0:(f 2 f ( p j ),f (T( p j+ )) (t)> -μ}+ inf{t>0:(f 2 f (T( p j)), f( p j+ ) (t)> -μ}]} Hence for all n,m N, n< m: Max[inf{t>0:(F T( p n),t( p m) (t)> -α}, c inf{t>0:(f 2 f (T( p n)), f (T( p m)) (t)> -α}] m- k(μ) Σ [ψ(φ(f(p j ))) - ψ(φ(f(p j+ )))] j = n k(α) [ψ(φ(f(p n ))) - ψ(φ(f(p m )))] for some α with 0< α j+ α k α, j = n,, m- and inf {t>0: F p n,p n+ (t) >-α} inf{t>0:(f p n,t( p n+) (t)> -μ} + inf{t>0:(f T( p n),t( p n+) (t)> -μ} + inf{t>0:(f T( p n), p n+ (t)> -μ { /2[inf{t>0:(F p n,t( p n+) (t)> -μ}+ inf{t>0:(f p n+,t( p n) (t)> -μ}] 3 k(α) [ψ(φ(f(p n ))) - ψ(φ( f(p n+ )))] Then, for n<m inf{t>0:(f T( p n),t( p m) (t)> -α} 3 k(α) [ψ(φ(f(p n ))) - ψ(φ( f(p m )))] Similarly, inf{t>0:(f 2 f (T( p n)), f (T( p n +)) (t)> -α} 3 k(α) [ψ(φ(f(p n ))) - ψ(φ( f(p m )))] Hence {p n } and { f(p n )}are cauchy sequences. Let lim p n = u and lim f(p n ) = v as n. Since f is closed therefore f(u) = v f (X ). By the continuity of ψ and lower semi continuity of φ, we have
5 Fixed point results in probabilistic space 24 ψ(φ(v)) lim ψ(φ(f (p n ))) = lim ψ(φ(f (p n+ ))) Let inf ψ(φ(f (x))) = λ 0 R. From ψ(φ(f (p n+ ))) λ 0 + /2 {ψ(φ(f (p n ))) - λ 0 }, we have lim ψ(φ(f (p n+ ))) λ 0 /2 + /2 lim ψ(φ(f (p n ))) = λ 0 /2 + /2 lim ψ(φ(f (p n+ ))). Finally, ψ(φ(f (u))) = ψ(φ(v)) lim ψ(φ(f (p n+ ))) λ 0 = inf ψ(φ(f (x))) ψ(φ(f (u))) which is contradiction. Therefore there exists an x 0 X such that inf ψ(φ(f (x))) = ψ(φ(f (x 0 ))). Theorem 2 : Let (X,F,Δ ) and (X 2,F 2,Δ 2 ) be two complete Menger probabilistic metric space with t-norm satisfying the condition (). Let f : X X 2 be a mapping, T:X X be a continuous mapping satisfying inf{t>0:f Tx,Ty (t) > -α} inf{t>0:/2(f x,ty (t)+ F Tx,y (t)) > -α} and inf{t>0:f 2 f (Tx), f (Ty) (t) > -α} inf{t>0:/2(f 2 x,ty (t)+ F 2 Tx,y (t))> -α} for all x,y in X and α (0,]. Let ψ: R R be a non decreasing continuous function, bounded from below and φ:f(x ) R a lower semi continuous function, bounded from below. Let S :X X be continuous mapping. Further, if S and T are quasi compatible and Max{/2[inf{t>0:(F x,tsx (t)> -α}+ inf{t>0:(f Tx,Sx (t)> -α}], c/2[[inf{t>0:(f 2 f (x),f (TSx) (t)> -α}+ inf{t>0:(f 2 f (Tx), f (Sxs) (t)> -α}]} k(α) [ψ(φ(f(x))) - ψ(φ(f(sx)))], for every x and α (0,],where c >0 is a given constant, then there exists unique common fixed point. Proof: By the theorem, we have inf ψ(φ(f (x))) = ψ(φ(f (x 0 ))). Suppose x 0 TSx 0 or Sx 0 Tx 0. Then for some α (0,] 0< /2[inf{t>0:(F x0,tsx0 (t)> -α}+ inf{t>0:(f Tx0,Sx0 (t)> -α}] k(α) [ψ(φ(f(x 0 ))) - ψ(φ(f(sx 0 )))] 0 which is the contradiction. Therefore x 0 = TSx 0 or Sx 0 = Tx 0 and also x 0 = Tx 0. Moreover for every α (0,] there exists μ (0, α] such that inf{t>0:(f x0,tx0 (t)> -α} inf{t>0:(f x0,tsx0 (t)> -μ}+ inf{t>0:(f TSx0,Tx0 (t)> -μ}] = inf{t>0:(f TSx0,Tx0 (t)> -μ}] /2[inf{t>0:(F Sx0,Tx0 (t)> -μ}+ inf{t>0:(f x0,tsx0 (t)> -μ}]] = 0. Thus x 0 = Tx 0 ( = Sx 0 ) Uniqueness can obtain by the given condition. Corollary:: Let (X,F,Δ ) and (X 2,F 2,Δ 2 ) be two complete Menger probabilistic metric space with t-norm satisfying the condition ().Let f : X X 2 be a closed mapping, and φ:f(x ) R a lower semi continuous function, bounded from below. Let S :X X be a mapping such that max{inf{t>0:(f S x,x (t)>-α}, c inf{t>0:(f 2 f (S(x)),f (x) (t)>-α}} k(α) [φ(f(x)) - φ(f(s(x))) for every x and α (0,],where c >0 is a given constant, then there exists unique common fixed point.
6 242 V. Ben Dhagat, S. Nath and N. Kumar Proof: On taking T = I and ψ = I in theorem 2. References [] K. Menger, Statistical metrics, Procedings of the National Academy of Sciences of the United state of America 28(942), [2] S. N. Mishra, Common fixed points of compatible mappings in PM- space, Mathematica Japonica 36 (99) no. 2, [3] B. Schweizer and A. Sklar, Statistical metric space, Pacific Journal of Mathematics 0(960), [4] W. Takahashi, Fixed Point Theory and Application, Pitman Res. Not.Math. Ser. 252(99), Received: March, 2009
Fixed point results in Fuzzy Menger space
Journal of Applied Mathematics & Bioinformatics, vol.5, no.1, 2015, 67-75 ISSN: 1792-6602 (print), 1792-6939 (online) Scienpress Ltd, 2015 Fixed point results in Fuzzy Menger space Ruchi Singh 1, A.D.
More informationA Fixed Point Theorem For Multivalued Maps In Symmetric Spaces
Applied Mathematics E-Notes, 4(2004), 26-32 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ A Fixed Point Theorem For Multivalued Maps In Symmetric Spaces Driss El
More informationFIXED POINT THEOREMS FOR LOCAL ALMOST CONTRACTIONS
Miskolc Mathematical Notes HU e-issn 1787-2413 Vol. 18 (2017), No. 1, pp. 499 506 DOI: 10.18514/MMN.2017.1905 FIXED POINT THEOREMS FOR LOCAL ALMOST CONTRACTIONS MONIKA ZAKANY Received 05 December, 2015
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 informationResearch Article Fixed Point Theorems for Nonlinear Contractions in Menger Spaces
Abstract and Applied Analysis Volume 2011, Article ID 143959, 18 pages doi:10.1155/2011/143959 Research Article Fixed Point Theorems for Nonlinear Contractions in Menger Spaces Jeong Sheok Ume Department
More informationFIXED POINT THEOREM USING COMPATIBILITY OF TYPE (A) AND WEAK COMPATIBILITY IN MENGER SPACE
www.arpapress.com/volumes/vol10issue3/ijrras_10_3_11.pdf FIXED POINT THEOREM USING COMPATIBILITY OF TYPE (A) AND WEAK COMPATIBILITY IN MENGER SPACE Bijendra Singh 1, Arihant Jain 2 and Javaid Ahmad Shah
More informationFixed Point Result for P-1 Compatible in Fuzzy Menger Space
Asian Journal of uzzy and Applied Mathematics (ISSN: 2321 564X) Volume 02 Issue 01, ebruary 2014 ixed Point Result for P-1 Compatible in uzzy Menger Space Rashmi Pathak 1, Manoj Kumar Shukla 2, Surendra
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 informationCOMMON FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE
Kragujevac Journal of Mathematics Volume 35 Number 3 (2011), Pages 463 470. COMMON FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE B. D. PANT, SUNNY CHAUHAN AND QAMAR ALAM Abstract. The notion of weakly
More informationOn Common Fixed Points in Menger Probabilistic Metric Spaces
Int. J. Contemp. Math. Sciences, Vol. 2, 2007, no. 8, 383-391 On Common Fixed Points in Menger Probabilistic Metric Spaces Servet Kutukcu Department of Mathematics, Faculty of Science and Arts Ondokuz
More informationCommon fixed point theorems in Menger space with special reference to coincidence points
Available online at www.pelagiaresearchlibrary.com Advances in Applied Science Research, 2015, 6(7):224-229 ISSN: 0976-8610 CODEN (USA): AASRFC Common fixed point theorems in Menger space with special
More informationFIXED POINT THEOREM USING WEAK COMPATIBILITY IN MENGER SPACE
ISSN 2320-9143 1 International Journal of Advance Research, IJOAR.org Volume 1, Issue 10, October 2013, Online: ISSN 2320-9143 FIXED POINT THEOREM USING WEAK COMPATIBILITY IN MENGER SPACE RAMESH BHINDE
More informationOn Uniform Limit Theorem and Completion of Probabilistic Metric Space
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 10, 455-461 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4120 On Uniform Limit Theorem and Completion of Probabilistic Metric Space
More informationCommon fixed Points for Multimaps in Menger Spaces
Qatar Uni. Sci. J. (2007), 27: 11-15 Common fixed Points for Multimaps in Menger Spaces Bhaana Deshpande Department of Mathematics, Got. Arts-Science P. G. College, Ratlam(M. P.), India E-Mail: bhanadeshpande@yahoo.com
More informationCommon Fixed Point Theorem for Six Maps in. d-complete Topological Spaces
Int. Journal of Math. Analysis, Vol. 6, 202, no. 4, 204-2047 Common Fixed Point Theorem for Six Maps in d-complete Topological Spaces Rahul Tiwari Department of Mathematical Sciences A.P.S. University,
More informationFUZZY H-WEAK CONTRACTIONS AND FIXED POINT THEOREMS IN FUZZY METRIC SPACES
Gulf Journal of Mathematics Vol, Issue 2 203 7-79 FUZZY H-WEAK CONTRACTIONS AND FIXED POINT THEOREMS IN FUZZY METRIC SPACES SATISH SHUKLA Abstract. The purpose of this paper is to introduce the notion
More informationFixed Point Results in Non-Archimedean Fuzzy Menger spaces
Fixed Point Results in Non-Archimedean Fuzzy Menger spaces Shailendra Kumar Patel,Manoj Shukla and R. P. Dubey Bhilai Institute of Tech., Raipur (C.G) India e-mail spskpatel@gmail.com Govt. Model Science
More informationCommon Fixed Point Theorem Satisfying Implicit Relation On Menger Space.
www.ijecs.in International Journal Of Engineering And Computer Science ISSN:2319-7242 Volume 5 Issue 09 September 2016 Page No.18180-18185 Common Fixed Point Theorem Satisfying Implicit Relation On Menger
More informationAvailable online at Advances in Fixed Point Theory, 2 (2012), No. 4, ISSN:
Available online at http://scik.org Advances in Fixed Point Theory, 2 (2012), No. 4, 452-463 ISSN: 1927-6303 SOME FIXED POINT RESULTS IN MENGER SPACES SUNNY CHAUHAN 1, SANDEEP BHATT 2, AND NEERAJ DHIMAN
More informationCOMMON FIXED POINTS FOR WEAKLY COMPATIBLE MAPS IN SYMMETRIC SPACES WITH APPLICATION TO PROBABILISTIC SPACES
Applied Mathematics E-Notes, 5(2005), 171-175 c ISSN 1607-2510 Available free at mirror sites of http://wwwmathnthuedutw/ amen/ COMMON FIXED POINTS FOR WEAKLY COMPATIBLE MAPS IN SYMMETRIC SPACES WITH APPLICATION
More informationLacunary Statistical Convergence on Probabilistic Normed Spaces
Int. J. Open Problems Compt. Math., Vol. 2, No.2, June 2009 Lacunary Statistical Convergence on Probabilistic Normed Spaces Mohamad Rafi Segi Rahmat School of Applied Mathematics, The University of Nottingham
More informationTHE EXISTENCE OF COMMON FIXED POINTS FOR FAINTLY COMPATIBLE MAPPINGS IN MENGER SPACES
International Journal of Pure and Applied Mathematics Volume 97 No. 1 2014, 37-48 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v97i1.5
More informationCOMMON FIXED POINT THEOREM FOR SUB COMPATIBLE AND SUB SEQUENTIALLY CONTINUOUS MAPS IN FUZZY METRIC SPACE USING IMPLICT RELATION
IJRRAS 9 (1) October 011 www.arpapress.com/volumes/vol9issue1/ijrras_9_1_10.pdf COMMON FIXED POINT THEOREM FOR SUB COMPATIBLE AND SUB SEQUENTIALLY CONTINUOUS MAPS IN FUZZY METRIC SPACE USING IMPLICT RELATION
More informationCOMMON FIXED POINT OF SEMI COMPATIBLE MAPS IN FUZZY METRIC SPACES
COMMON FIXED POINT OF SEMI COMPATIBLE MAPS IN FUZZY METRIC SPACES 1 M. S. Chauhan, 2 V. H. Badshah, 3 Virendra Singh Chouhan* 1 Department of Mathematics, Govt. Nehru PG College, Agar Malwa (India) 2 School
More informationCommon Fixed Point Theorems for Two Pairs of Weakly Compatible Mappings in Fuzzy Metric Spaces Using (CLR ST ) Property
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 12, Issue 6 Ver. I (Nov. - Dec.2016), PP 66-71 www.iosrjournals.org Common Fixed Point Theorems for Two Pairs of Weakly
More informationOn Some Results in Fuzzy Metric Spaces
Theoretical Mathematics & Applications, vol.4, no.3, 2014, 79-89 ISSN: 1792-9687 (print), 1792-9709 (online) Scienpress Ltd, 2014 On Some Results in Fuzzy Metric Spaces Arihant Jain 1, V. H. Badshah 2
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 informationConvergence of Common Fixed Point Theorems in Fuzzy Metric Spaces
Journal of mathematics and computer science 8 (2014), 93-97 Convergence of Common Fixed Point Theorems in Fuzzy Metric Spaces Virendra Singh Chouhan Department of Mathematics Lovely Professional University,
More informationAvailable online at Adv. Fixed Point Theory, 3 (2013), No. 4, ISSN:
Available online at http://scik.org Adv. Fixed Point Theory, 3 (2013), No. 4, 595-599 ISSN: 1927-6303 A COMMON FIXED POINT THEOREM UNDER ϕ-contractive CONDITIONS PH.R. SINGH 1,, AND M.R. SINGH 2, 1 Department
More informationJournal of Shivaji University (Science & Technology) SOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION.
SOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION. Deepti Thakur and Sushil Sharma Department of Mathematics, Madhav Vigyan Mahavidhyalaya, Vikram University, Ujjain
More informationResearch Article The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with w-distances
Applied Mathematics Volume 2012, Article ID 161470, 11 pages doi:10.1155/2012/161470 Research Article The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with w-distances Hossein
More informationA FIXED POINT THEOREM IN MENGER SPACES
International Mathematical Forum, 1, 2006, no. 32, 1543-1554 A FIXED POINT THEOREM IN MENGER SPACES Servet Kutukcu Department of Mathematics, Faculty of Science and Arts, Ondokuz Mayis University, Kurupelit,
More informationIntuitionistic Fuzzy Metric Groups
454 International Journal of Fuzzy Systems, Vol. 14, No. 3, September 2012 Intuitionistic Fuzzy Metric Groups Banu Pazar Varol and Halis Aygün Abstract 1 The aim of this paper is to introduce the structure
More informationA Common Fixed Point Theorems in Menger(PQM) Spaces with Using Property (E.A)
Int. J. Contemp. Math. Sciences, Vol. 6, 2011, no. 4, 161-167 A Common Fixed Point Theorems in Menger(PQM) Spaces with Using Property (E.A) Somayeh Ghayekhloo Member of young Researchers club, Islamic
More informationFixed Point Theorems via Absorbing Maps
Thai Journal of Mathematics Volume 6 (2008) Number 1 : 49 60 www.math.science.cmu.ac.th/thaijournal Fixed Point Theorems via Absorbing Maps U. Mishra, A. S. Ranadive and D. Gopal Abstract : The purpose
More informationSome Basic Properties of D -fuzzy metric spaces and Cantor s Intersection Theorem
Advances in Fuzzy Mathematics (AFM). ISSN 0973-533X Volume 13, Number 1 (2018), pp. 49 58 Research India Publications http://www.ripublication.com/afm.htm Some Basic Properties of D -fuzzy metric spaces
More informationFixed point theorem for F w -contractions in complete metric spaces
Journal Nonlinear Analysis and Application 2013 (2013) 1-6 Available online at www.ispacs.com/jnaa Volume 2013, Year 2013 Article ID jnaa-00211, 6 Pages doi:10.5899/2013/jnaa-00211 Research Article Fixed
More informationarxiv: v1 [math.gm] 20 Oct 2014
arxiv:1410.5748v1 [math.gm] 20 Oct 2014 A CHARACTERIZATION OF CAUCHY SEQUENCES IN FUZZY METRIC SPACES AND ITS APPLICATION TO FUZZY FIXED POINT THEORY MORTAZA ABTAHI Abstract. We introduce the concept of
More informationCOMMON RANDOM FIXED POINTS UNDER QUASI CONTRACTION CONDITIONS IN SYMMETRIC SPACES
Available online at http://scik.org Adv. Fixed Point Theory, 7 (2017), No. 3, 451-457 ISSN: 1927-6303 COMMON RANDOM FIXED POINTS UNDER QUASI CONTRACTION CONDITIONS IN SYMMETRIC SPACES Maulana Azad National
More informationUniform Convergence and Uniform Continuity in Generalized Metric Spaces
Int. Journal of Math. Analysis, Vol. 5, 2011, no. 6, 285-296 Uniform Convergence and Uniform Continuity in Generalized Metric Spaces Abdul Mohamad Department of Mathematics and Statistics Sultan Qaboos
More informationSemigroup, monoid and group models of groupoid identities. 1. Introduction
Quasigroups and Related Systems 16 (2008), 25 29 Semigroup, monoid and group models of groupoid identities Nick C. Fiala Abstract In this note, we characterize those groupoid identities that have a (nite)
More informationSome Common Fixed Point Theorems for Self Mappings in Vector Metric Spaces
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 35, 1735-1742 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2013.3475 Some Common Fixed Point Theorems for Self Mappings in Vector Metric
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 informationSemi-Compatibility, Weak Compatibility and. Fixed Point Theorem in Fuzzy Metric Space
International Mathematical Forum, 5, 2010, no. 61, 3041-3051 Semi-Compatibility, Weak Compatibility and Fixed Point Theorem in Fuzzy Metric Space Bijendra Singh*, Arihant Jain** and Aijaz Ahmed Masoodi*
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 informationA Generalized Contraction Mapping Principle
Caspian Journal of Applied Mathematics, Ecology and Economics V. 2, No 1, 2014, July ISSN 1560-4055 A Generalized Contraction Mapping Principle B. S. Choudhury, A. Kundu, P. Das Abstract. We introduce
More informationCommon Fixed Point Theorems on Fuzzy Metric Spaces Using Implicit Relation
Math Sci Lett 1 No 2 89-96 (2012) 89 Common Fixed Point Theorems on Fuzzy Metric Spaces Using Implicit Relation Sunny Chauhan 1 and Neeraj Dhiman 2 1 Near Nehru Training Centre H No 274 Nai Basti B-14
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 informationCOMMON FIXED POINT THEOREMS FOR CYCLIC WEAK
Available online at http://scik.org Adv. Inequal. Appl. 204, 204:38 ISSN: 2050-746 COMMON FIXED POINT THEOREMS FOR CYCLIC WEAK, ψ-contractions IN MENGER SPACES S.M. ROOSEVELT,, K.S. DERSANAMBIKA 2 Department
More informationFixed Point Theorems with Implicit Function in Metric Spaces
Int. J. Contemp. Math. Sciences, Vol. 8, 013, no. 17, 833-841 HIKARI Ltd, www.m-hiari.com http://dx.doi.org/10.1988/ijcms.013.3894 Fixed Point Theorems with Implicit Function in Metric Spaces A. Muraliraj
More informationInternational Journal of Mathematical Archive-5(10), 2014, Available online through ISSN
International Journal of Mathematical Archive-5(10), 2014, 217-224 Available online through www.ijma.info ISSN 2229 5046 COMMON FIXED POINT OF WEAKLY COMPATIBLE MAPS ON INTUITIONISTIC FUZZY METRIC SPACES
More informationarxiv: v2 [math.gn] 17 Apr 2017
New Generalized Fixed Point Results on S b -Metric Spaces arxiv:1703.01868v2 [math.gn] 17 Apr 2017 NİHAL TAŞ and NİHAL YILMAZ ÖZGÜR Department of Mathematics, Balıkesir University, Balıkesir 10145, Turkey
More informationCommon Random Fixed Point theorem for compatible random multivalued operators
IOSR Journal of Mathematics (IOSR-JM) ISSN: 78-578. Volume, Issue (Sep-Oct. 0), PP9-4 Common Random Fixed Point theorem for compatible random multivalued operators Dr. Neetu Vishwakarma Abstract: The aim
More informationL -Random and Fuzzy Normed Spaces and Classical Theory
CUBO A Mathematical Journal Vol.12, N ō 03, (71 81). October 2010 L -Random and Fuzzy Normed Spaces and Classical Theory DONAL O REGAN Department of Mathematics, National University of Ireland, Galway,
More informationA Common Fixed Point Theorem Satisfying Integral Type Implicit Relations
Applied Mathematics E-Notes, 7(27, 222-228 c ISSN 167-251 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ A Common Fixed Point Theorem Satisfying Integral Type Implicit Relations Hemant
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 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 informationFixed Point Theorem in Fuzzy Metric Space Using (CLRg) Property
International Journal of Engineering Science Invention ISSN (Online): 2319 6734, ISSN (Print): 2319 6726 Volume 5 Issue 4 April 2016 PP.35-39 Fixed Point Theorem in Fuzzy Metric Space Using (CLRg) Property
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 information(, q)-fuzzy Ideals of BG-algebras with respect to t-norm
NTMSCI 3, No. 4, 196-10 (015) 196 New Trends in Mathematical Sciences http://www.ntmsci.com (, q)-fuzzy Ideals of BG-algebras with respect to t-norm Saidur R. Barbhuiya Department of mathematics, Srikishan
More informationCOMMON FIXED POINT THEOREM FOR FOUR MAPPINGS IN INTUITIONISTIC FUZZY METRIC SPACE USING ABSORBING MAPS
www.arpapress.com/volumes/vol10issue2/ijrras_10_2_12.pdf COMMON FIXED POINT THEOREM FOR FOUR MAPPINGS IN INTUITIONISTIC FUZZY METRIC SPACE USING ABSORBING MAPS Mona Verma 1 & R. S. Chandel 2 1 Technocrats
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 informationIntroduction to Functional Analysis
Introduction to Functional Analysis Carnegie Mellon University, 21-640, Spring 2014 Acknowledgements These notes are based on the lecture course given by Irene Fonseca but may differ from the exact lecture
More informationWEAK CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS WITH NONLINEAR OPERATORS IN HILBERT SPACES
Fixed Point Theory, 12(2011), No. 2, 309-320 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html WEAK CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS WITH NONLINEAR OPERATORS IN HILBERT SPACES S. DHOMPONGSA,
More informationSOME COMMON FIXED POINT THEOREMS IN FUZZY 2-METRIC SPACES UNDER STRICT CONTRACTIVE CONDITIONS FOR MAPPINGS SATISFYING NEW PROPERTY
SOME COMMON FIXED POINT THEOREMS IN FUZZY 2-METRIC SPACES UNDER STRICT CONTRACTIVE CONDITIONS FOR MAPPINGS SATISFYING NEW PROPERTY *Amita Joshi Department of Mathematics, IPS Academy, ISLE, Indore, India
More informationResearch Article Coupled Fixed Point Theorems for a Pair of Weakly Compatible Maps along with CLRg Property in Fuzzy Metric Spaces
Applied Mathematics Volume 2012, Article ID 961210, 13 pages doi:10.1155/2012/961210 Research Article Coupled Fixed Point Theorems for a Pair of Weakly Compatible Maps along with CLRg Property in Fuzzy
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 informationAvailable online at J. Nonlinear Sci. Appl., 10 (2017), Research Article
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 2719 2726 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa An affirmative answer to
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 informationModular cone metric spaces
Pure and Applied Mathematics Journal 2013; 2(6): 191-196 Published online January 30, 2014 (http://www.sciencepublishinggroup.com/j/pamj) doi: 10.11648/j.pamj.20130206.14 Modular cone metric spaces Saeedeh
More informationResearch Article Some Generalizations of Fixed Point Results for Multivalued Contraction Mappings
International Scholarly Research Network ISRN Mathematical Analysis Volume 2011, Article ID 924396, 13 pages doi:10.5402/2011/924396 Research Article Some Generalizations of Fixed Point Results for Multivalued
More informationFixed point theorems in fuzzy metric spaces using (CLRG) property
Available online at www.pelagiaresearchlibrary.com Advances in Applied Science Research, 2015, 6(6):17-22 ISSN: 0976-8610 CODEN (USA): AASRFC Fixed point theorems in fuzzy metric spaces using (CLRG) property
More informationCompatible Mappings of Type (A 1) and Type (A 2) and Common Fixed Points in Fuzzy Metric Spaces
International Mathematical Forum, 2, 2007, no. 11, 515-524 Compatible Mappings of Type (A 1) and Type (A 2) and Common Fixed Points in Fuzzy Metric Spaces M. S. Khan 1 Department of Mathematics and Statistics
More informationOn Linear Operators with Closed Range
Journal of Applied Mathematics & Bioinformatics, vol.1, no.2, 2011, 175-182 ISSN: 1792-6602 (print), 1792-6939 (online) International Scientific Press, 2011 On Linear Operators with Closed Range P. Sam
More informationCommon Fixed Point Theory in Modified Intuitionistic Probabilistic Metric Spaces with Common Property (E.A.)
Sahand Communications in Mathematical Analysis SCMA Vol. 13 No. 1 2019, 31-50 http://scma.maragheh.ac.ir DOI: 10.22130/scma.2018.30018 Common Fixed Point Theory in Modified Intuitionistic Probabilistic
More informationKirk s Fixed Point Theorem in Generating Spaces of Semi-Norm Family
Gen. Math. Notes, Vol. 21, No. 2, April 2014, pp.1-13 ISSN 2219-7184; Copyright c ICSRS Publication, 2014 www.i-csrs.org Available free online at http://www.geman.in Kirk s Fixed Point Theorem in Generating
More informationarxiv: v1 [math.gn] 5 Apr 2013
Fixed Points for Ćirić-G-Contractions in Uniform Spaces Endowed with a Graph arxiv:1304.1721v1 [math.gn] 5 Apr 2013 Aris Aghanians 1, Kamal Fallahi 1, Kourosh Nourouzi 1, Ram U Verma 2 1 Department of
More informationFinal Exam Practice Problems Math 428, Spring 2017
Final xam Practice Problems Math 428, Spring 2017 Name: Directions: Throughout, (X,M,µ) is a measure space, unless stated otherwise. Since this is not to be turned in, I highly recommend that you work
More informationOn Generalized Probabilistic Normed Spaces
International Mathematical Forum, Vol. 6, 2011, no. 42, 2073-2078 On Generalized Probabilistic Normed Spaces Ioan Goleţ Department of Mathematics, Politehnica University 300006 Timişoara, Romania ioan.golet@mat.upt.ro
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 informationConvergence of sequences, limit of functions, continuity
Convergence of sequences, limit of functions, continuity With the definition of norm, or more precisely the distance between any two vectors in R N : dist(x, y) 7 x y 7 [(x 1 y 1 ) 2 + + (x N y N ) 2 ]
More informationCOMMON FIXED POINT THEOREMS FOR A PAIR OF COUNTABLY CONDENSING MAPPINGS IN ORDERED BANACH SPACES
Journal of Applied Mathematics and Stochastic Analysis, 16:3 (2003), 243-248. Printed in the USA c 2003 by North Atlantic Science Publishing Company COMMON FIXED POINT THEOREMS FOR A PAIR OF COUNTABLY
More information4.6. Linear Operators on Hilbert Spaces
4.6. Linear Operators on Hilbert Spaces 1 4.6. Linear Operators on Hilbert Spaces Note. This section explores a number of different kinds of bounded linear transformations (or, equivalently, operators
More informationCommon Fixed Point Theorems in Non-Archimedean. Menger PM-Spaces
Iteratioal Mathematical Forum, Vol. 6, 0, o. 40, 993-000 Commo Fixed Poit Theorems i No-Archimedea Meer PM-Spaces M. Alamir Kha Departmet of Mathematics, Eritrea Istitute of Techoloy Asmara, Eritrea (N.
More information1 Topology Definition of a topology Basis (Base) of a topology The subspace topology & the product topology on X Y 3
Index Page 1 Topology 2 1.1 Definition of a topology 2 1.2 Basis (Base) of a topology 2 1.3 The subspace topology & the product topology on X Y 3 1.4 Basic topology concepts: limit points, closed sets,
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 informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 4, 2011
Some common fixed point theorems for occasionally weakly compatible mappings in Fuzzy metric spaces Malhotra S.K 1, Navin Verma 2, Ravindra Sen 3 1- Department of Mathematics, Govt. S.G.S.P.G. College
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 informationLecture 2. Econ August 11
Lecture 2 Econ 2001 2015 August 11 Lecture 2 Outline 1 Fields 2 Vector Spaces 3 Real Numbers 4 Sup and Inf, Max and Min 5 Intermediate Value Theorem Announcements: - Friday s exam will be at 3pm, in WWPH
More informationFUZZY BCK-FILTERS INDUCED BY FUZZY SETS
Scientiae Mathematicae Japonicae Online, e-2005, 99 103 99 FUZZY BCK-FILTERS INDUCED BY FUZZY SETS YOUNG BAE JUN AND SEOK ZUN SONG Received January 23, 2005 Abstract. We give the definition of fuzzy BCK-filter
More informationCommon Fixed Point Theorems for Generalized Fuzzy Contraction Mapping in Fuzzy Metric Spaces
Volume 119 No. 12 2018, 14643-14652 ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Common Fixed Point Theorems for Generalized Fuzzy Contraction Mapping in Fuzzy Metric Spaces 1 R.
More informationCommon Fixed Point Theorem in Complex Valued Metric Spaces
ISSN: 219-875 (An ISO 297: 2007 Certified Organization) Vol. 2, Issue 12, December 201 Common Fixed Point Theorem in Complex Valued Metric Spaces Dr. Yogita R. Sharma Head, Department of Mathematics, Saffrony
More informationFuzzy fixed point of multivalued Ciric type fuzzy contraction mappings in b-metric spaces
Global Journal of Pure and Applied Mathematics. ISSN 0973-768 Volume, Number (06), pp. 307-36 Research India Publications http://www.ripublication.com Fuzzy fixed point of multivalued Ciric type fuzzy
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 informationMAS3706 Topology. Revision Lectures, May I do not answer enquiries as to what material will be in the exam.
MAS3706 Topology Revision Lectures, May 208 Z.A.Lykova It is essential that you read and try to understand the lecture notes from the beginning to the end. Many questions from the exam paper will be similar
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 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 informationOn Generalized Fuzzy Normed Spaces
International Mathematical Forum, 4, 2009, no. 25, 1237-1242 On Generalized Fuzzy Normed Spaces Ioan Goleţ Department of Mathematics Politehnica University 300006 Timişoara, Romania ioan.golet@mat.upt.ro
More informationViscosity approximation methods for equilibrium problems and a finite family of nonspreading mappings in a Hilbert space
44 2 «Æ Vol.44, No.2 2015 3 ADVANCES IN MATHEMATICS(CHINA) Mar., 2015 doi: 10.11845/sxjz.2015056b Viscosity approximation methods for equilibrium problems and a finite family of nonspreading mappings in
More informationSome Fixed Point Theorems in Generating Polish Space of Quasi Metric Family
Global ad Stochastic Aalysis Special Issue: 25th Iteratioal Coferece of Forum for Iterdiscipliary Mathematics Some Fied Poit Theorems i Geeratig Polish Space of Quasi Metric Family Arju Kumar Mehra ad
More information