• Title/Summary/Keyword: Common fixed point

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COMMON FIXED POINT THEOREM FOR MULTIMAPS ON MENGER L-FUZZY METRIC SPACE

  • Deshpande, Bhavana;Chouhan, Suresh
    • The Pure and Applied Mathematics
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    • v.20 no.1
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    • pp.11-23
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    • 2013
  • In this paper, we obtain a common fixed point theorem for multivalued mappings in a complete Menger $\mathcal{L}$-fuzzy metric space. $\mathcal{L}$-fuzzy metric space is a generalization of fuzzy metric spaces and intuitionistic fuzzy metric spaces. We extend and generalize the results of Kubiaczyk and Sharma [24], Sharma, Kutukcu and Rathore [34].

TRIPLED COINCIDENCE AND COMMON TRIPLED FIXED POINT THEOREM FOR HYBRID PAIR OF MAPPINGS SATISFYING NEW CONTRACTIVE CONDITION

  • Deshpande, Bhavana;Handa, Amrish
    • East Asian mathematical journal
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    • v.32 no.5
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    • pp.701-716
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    • 2016
  • We establish a tripled coincidence and common tripled fixed point theorem for hybrid pair of mappings satisfying new contractive condition. To find tripled coincidence points, we do not use the continuity of any mapping involved therein. An example is also given to validate our result. We improve, extend and generalize several known results.

COMMON COUPLED FIXED POINT FOR HYBRID PAIR OF MAPPINGS UNDER GENERALIZED NONLINEAR CONTRACTION

  • Deshpande, Bhavana;Handa, Amrish
    • East Asian mathematical journal
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    • v.31 no.1
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    • pp.77-89
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    • 2015
  • We establish a coupled coincidence and common coupled fixed point theorem for hybrid pair of mappings under generalized non-linear contraction. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

APPLICATION OF GENERALIZED WEAK CONTRACTION IN INTEGRAL EQUATION

  • Amrish Handa
    • The Pure and Applied Mathematics
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    • v.30 no.3
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    • pp.249-267
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    • 2023
  • This manuscript is divided into three segments. In the first segment, we prove a unique common fixed point theorem satisfying generalized weak contraction on partially ordered metric spaces and also give an example to support our results presented here. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of integral equation as an application. Our results generalize, extend and improve several well-known results of the existing literature.

COMMON n-TUPLED FIXED POINT THEOREM UNDER GENERALIZED MIZOGUCHI-TAKAHASHI CONTRACTION FOR HYBRID PAIR OF MAPPINGS

  • Deshpande, Bhavana;Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.29 no.1
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    • pp.1-17
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    • 2022
  • We establish a common n-tupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction. An example is given to validate our results. We improve, extend and generalize several known results.

A VISCOSITY APPROXIMATIVE METHOD TO CES$\`{A}$RO MEANS FOR SOLVING A COMMON ELEMENT OF MIXED EQUILIBRIUM, VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS

  • Jitpeera, Thanyarat;Katchang, Phayap;Kumam, Poom
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.227-245
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    • 2011
  • In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.