• Title/Summary/Keyword: weak common fixed point

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A GENERALIZED COMMON FIXED POINT THEOREM FOR TWO FAMILIES OF SELF-MAPS

  • PHANEENDRA, T.
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.1839-1854
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    • 2015
  • Brief developments in metrical fixed point theory are covered and a significant generalization of recent results obtained in [18], [27], [32] and [33] is established through an extension of the property (EA) to two sequences of self-maps using the notions of weak compatibility and implicit relation.

WEAK AND STRONG CONVERGENCE OF THREE-STEP ITERATIONS WITH ERRORS FOR TWO ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

  • Jeong, Jae-Ug
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.325-336
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    • 2008
  • In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

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WEAK CONVERGENCE TO COMMON FIXED POINTS OF COUNTABLE NONEXPANSIVE MAPPINGS AND ITS APPLICATIONS

  • Kimura, Yasunori;Takahashi, Wataru
    • Journal of the Korean Mathematical Society
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    • v.38 no.6
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    • pp.1275-1284
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    • 2001
  • In this paper, we introduce an iteration generated by countable nonexpansive mappings and prove a weak convergence theorem which is connected with the feasibility problem. This result is used to solve the problem of finding a solution of the countable convex inequality system and the problem of finding a common fixed point for a commuting countable family of nonexpansive mappings.

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FIXED POINT THEOREMS IN ORDERED b-METRIC SPACES WITH ALTERNATING DISTANCE FUNCTIONS

  • Bouhafs, Radia;Tallafha, Abdalla Ahmed;Shatanawi, Wasfi
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.3
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    • pp.581-600
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    • 2021
  • In this paper we obtain a unique common fixed point theorem for four self-maps which are involved in (𝜙, 𝜓)-weak contraction of a partially ordered b-metric space. The necessary condition has been given to a space for the existence of an unique common fixed of the maps. And our work changed conditions and nonlinear contraction, and search for the unique common fixed point of the maps.

UTILIZING WEAK 𝜓 - 𝜑 CONTRACTION ON FUZZY METRIC SPACES

  • Amrish Handa
    • The Pure and Applied Mathematics
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    • v.30 no.3
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    • pp.309-336
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    • 2023
  • We establish some common fixed point theorems satisfying weak ψ - ϕ contraction on partially ordered non-Archimedean fuzzy metric spaces. By using this results we show the existence of fixed point on the domain of words and apply this approach to deduce the existence of solution for some recurrence equations associated to the analysis of Quicksort algorithms and divide and Conquer algorithms, respectively and also give an example to show the usefulness of our hypothesis. Our results generalize, extend and improve several well-known results of the existing literature in fixed point theory.

CONVERGENCE TO COMMON FIXED POINTS FOR A FINITE FAMILY OF GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES

  • Saluja, G.S.
    • East Asian mathematical journal
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    • v.29 no.1
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    • pp.23-37
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    • 2013
  • The purpose of this paper is to study an implicit iteration process with errors and establish weak and strong convergence theorems to converge to common fixed points for a finite family of generalized asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve and generalize some known results from the existing literature.

WEAK CONVERGENCE OF A HYBRID ITERATIVE SCHEME WITH ERRORS FOR EQUILIBRIUM PROBLEMS AND COMMON FIXED POINT PROBLEMS

  • Kim, Seung-Hyun;Lee, Byung-Soo
    • The Pure and Applied Mathematics
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    • v.21 no.3
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    • pp.195-206
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    • 2014
  • In this paper, we consider, under a hybrid iterative scheme with errors, a weak convergence theorem to a common element of the set of a finite family of asymptotically k-strictly pseudo-contractive mappings and a solution set of an equilibrium problem for a given bifunction, which is the approximation version of the corresponding results of Kumam et al.