• 제목/요약/키워드: Common fixed point

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Some Common Fixed Point Theorems using Compatible Maps in Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제11권2호
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    • pp.108-112
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    • 2011
  • Kaneko et a1.[4] etc many authors extended with multi-valued maps for the notion of compatible maps in complete metric space. Recently, O'Regan et a1.[5] presented fixed point and homotopy results for compatible single-valued maps on complete metric spaces. In this paper, we will establish some common fixed point theorems using compatible maps in intuitionistic fuzzy metric space.

COMMON FIXED POINT OF GENERALIZED ASYMPTOTIC POINTWISE (QUASI-) NONEXPANSIVE MAPPINGS IN HYPERBOLIC SPACES

  • Saleh, Khairul;Fukhar-ud-din, Hafiz
    • Korean Journal of Mathematics
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    • 제28권4호
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    • pp.915-929
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    • 2020
  • We prove a fixed point theorem for generalized asymptotic pointwise nonexpansive mapping in the setting of a hyperbolic space. A one-step iterative scheme approximating common fixed point of two generalized asymptotic pointwise (quasi-) nonexpansive mappings in this setting is provided. We obtain ∆-convergence and strong convergence theorems of the iterative scheme for two generalized asymptotic pointwise nonexpansive mappings in the same setting. Our results generalize and extend some related results in the literature.

COMMON FIXED POINT THEOREMS UNDER RATIONAL CONTRACTIONS IN COMPLEX VALUED EXTENDED b-METRIC SPACES

  • Vairaperumal, V.;Raj, J. Carmel Pushpa;Joseph, J. Maria;Marudai, M.
    • Nonlinear Functional Analysis and Applications
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    • 제26권4호
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    • pp.685-700
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    • 2021
  • In this paper, we discuss the existence and uniqueness of fixed point and common fixed point theorems in complex valued extended b-metric spaces for a pair of mappings satisfying some rational contraction conditions which generalized and unify some well-known results in the literature.

COMMON FIXED POINT THEOREMS FOR A CLASS OF WEAKLY COMPATIBLE MAPPINGS IN D-METRIC SPACES

  • Kim, Jong-Kyu;Sedghi, Shaban;Shobe, Nabi
    • East Asian mathematical journal
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    • 제25권1호
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    • pp.107-117
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    • 2009
  • In this paper, we give some new definitions of D-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly compatible mappings in complete D-metric spaces. We get some improved versions of several fixed point theorems in complete D-metric spaces.

COMMON FIXED POINTS FOR COMPATIBLE MAPPINGS OF TYPE(A) IN 2-METRIC SPACES

  • WANG, WEN-ZUO
    • 호남수학학술지
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    • 제22권1호
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    • pp.91-97
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    • 2000
  • In this paper we obtain a criterion for the existence of a common fixed point of a pair of mappings in 2-metric spaces. Our result generalizes a number of fixed point theorems given by Imdad, Khan and Khan [1], Kahn and Fisher [2], Kubiak [3], Rhoades [5], and Singh, Tiwari and Gupta [6].

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Some Common Fixed Points for Type(β) Compatible Maps in an Intuitionistic Fuzzy Metric Space

  • Park, Jong Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제13권2호
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    • pp.147-153
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    • 2013
  • Previously, Park et al. (2005) defined an intuitionistic fuzzy metric space and studied several fixed-point theories in this space. This paper provides definitions and describe the properties of type(${\beta}$) compatible mappings, and prove some common fixed points for four self-mappings that are compatible with type(${\beta}$) in an intuitionistic fuzzy metric space. This paper also presents an example of a common fixed point that satisfies the conditions of Theorem 4.1 in an intuitionistic fuzzy metric space.

COMMON FIXED POINT THEOREMS WITH APPLICATIONS TO THE SOLUTIONS OF FUNCTIONAL EQUATIONS ARISING IN DYNAMIC PROGRAMMING

  • Liu, Zeqing;Liu, Min;Kim, Hyeong-Kug;Kang, Shin-Min
    • 대한수학회논문집
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    • 제24권1호
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    • pp.67-83
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    • 2009
  • Several common fixed point theorems for a few contractive type mappings in complete metric spaces are established. As applications, the existence and uniqueness of common solutions for certain systems of functional equations arising in dynamic programming are discussed.

FIXED POINT AND PERIODIC POINT THEOREMS ON METRIC SPACES

  • Cho, Seong-Hoon;Park, Dong-Gon
    • 충청수학회지
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    • 제26권1호
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    • pp.1-16
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    • 2013
  • The aim of this paper is to establish a new fixed point theorem for a set-valued mapping defined on a metric space satisfying a weak contractive type condition and to establish a new common fixed point theorem for a pair of set-valued mappings defined on a metric space satisfying a weak contractive type inequality. And we give periodic point theorems for single-valued mappings defined on a metric space satisfying weak contractive type conditions.

COMMON FIXED POINT THEOREMS IN THE SETTING OF EXTENDED QUASI b-METRIC SPACES UNDER EXTENDED A-CONTRACTION MAPPINGS

  • Amina-Zahra Rezazgui;Wasfi Shatanawi;Abdalla Ahmad Tallafha
    • Nonlinear Functional Analysis and Applications
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    • 제28권1호
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    • pp.251-263
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    • 2023
  • In the setting of extended quasi b-metric spaces, we introduce a new concept called "extended A-contraction". We then use our concept to prove a common fixed point result for a pair of self mappings under a set of conditions. Also, we provide the concepts of extended B-contraction and extended R-contraction. We then establish a common fixed point under these new contractions. Our results generalize many existing result of fixed point in metric spaces. Furthermore, we give an example to illustrate and support our result.

NONLINEAR ALGORITHMS FOR A COMMON SOLUTION OF A SYSTEM OF VARIATIONAL INEQUALITIES, A SPLIT EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEMS

  • Jeong, Jae Ug
    • Korean Journal of Mathematics
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    • 제24권3호
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    • pp.495-524
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    • 2016
  • In this paper, we propose an iterative algorithm for finding a common solution of a system of generalized equilibrium problems, a split equilibrium problem and a hierarchical fixed point problem over the common fixed points set of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently.