• Title/Summary/Keyword: Weak Point

Search Result 1,051, Processing Time 0.026 seconds

A NEW GENERALIZED RESOLVENT AND APPLICATION IN BANACH MAPPINGS

  • Wang, Xian;Chen, Jun-Min;He, Zhen
    • East Asian mathematical journal
    • /
    • v.30 no.1
    • /
    • pp.69-77
    • /
    • 2014
  • In this paper, we introduce a new generalized resolvent in a Banach space and discuss its some properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.

APPLICATION OF GENERALIZED WEAK CONTRACTION IN INTEGRAL EQUATION

  • Amrish Handa
    • The Pure and Applied Mathematics
    • /
    • v.30 no.3
    • /
    • pp.249-267
    • /
    • 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.

FIXED POINT THEOREMS FOR WEAK CONTRACTION IN INTUITIONISTIC FUZZY METRIC SPACE

  • Vats, Ramesh Kumar;Grewal, Manju
    • Honam Mathematical Journal
    • /
    • v.38 no.2
    • /
    • pp.337-357
    • /
    • 2016
  • The notion of weak contraction in intuitionistic fuzzy metric space is well known and its study is well entrenched in the literature. This paper introduces the notion of (${\psi},{\alpha},{\beta}$)-weak contraction in intuitionistic fuzzy metric space. In this contrast, we prove certain coincidence point results in partially ordered intuitionistic fuzzy metric spaces for functions which satisfy a certain inequality involving three control functions. In the course of investigation, we found that by imposing some additional conditions on the mappings, coincidence point turns out to be a fixed point. Moreover, we establish a theorem as an application of our results.

On Fixed Point Theorem of Weak Compatible Maps of Type(γ) in Complete Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
    • /
    • v.11 no.1
    • /
    • pp.38-43
    • /
    • 2011
  • In this paper, we give definitions of compatible mappings of type(${\gamma}$) in intuitionistic fuzzy metric space and obtain common fixed point theorem under the conditions of weak compatible mappings of type(${\gamma}$) in complete intuitionistic fuzzy metric space. Our research generalize, extend and improve the results given by Sedghi et.al.[12].

COMMON FIXED POINTS OF WEAK-COMPATIBLE MAPS ON D-METRIC SPACE

  • Singh, Bijendra;Jain, Shobha
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.17 no.2
    • /
    • pp.111-124
    • /
    • 2004
  • In [4], Dhage proved a result for common fixed point of two self-maps satisfying a contractive condition in D-metric spaces. This note proves a fixed point theorem for five self-maps under weak-compatibility in D-metric space which improves and generalizes the above mentioned result.

  • PDF

COINCIDENCE AND FIXED POINT RESULTS FOR GENERALIZED WEAK CONTRACTION MAPPING ON b-METRIC SPACES

  • Malkawi, Abed Al-Rahman M.;Talafhah, Abdallah;Shatanawi, Wasfi
    • Nonlinear Functional Analysis and Applications
    • /
    • v.26 no.1
    • /
    • pp.177-195
    • /
    • 2021
  • In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

UTILIZING WEAK 𝜓 - 𝜑 CONTRACTION ON FUZZY METRIC SPACES

  • Amrish Handa
    • The Pure and Applied Mathematics
    • /
    • v.30 no.3
    • /
    • pp.309-336
    • /
    • 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.

(DS)-WEAK COMMUTATIVITY CONDITION AND COMMON FIXED POINT IN INTUITIONISTIC MENGER SPACES

  • Sharma, Sushil;Deshpande, Bhavana;Chouhan, Suresh
    • The Pure and Applied Mathematics
    • /
    • v.18 no.3
    • /
    • pp.201-217
    • /
    • 2011
  • The aim of this paper is to define a new commutativity condition for a pair of self mappings i.e., (DS)-weak commutativity condition, which is weaker that compatibility of mappings in the settings of intuitionistic Menger spaces. We show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic Menger spaces without assuming continuity of any mapping. To prove the result we use (DS)-weak commutativity condition for mappings. We also give examples to validate our results.

CONVERGENCE THEOREMS FOR TWO FAMILIES OF WEAK RELATIVELY NONEXPANSIVE MAPPINGS AND A FAMILY OF EQUILIBRIUM PROBLEMS

  • Zhang, Xin;Su, Yongfu
    • Communications of the Korean Mathematical Society
    • /
    • v.25 no.4
    • /
    • pp.583-607
    • /
    • 2010
  • The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced in [W. Takahashi and K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Article ID 528476, 11 pages; doi:10.1155/2008/528476] and [Y. Su, Z. Wang, and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no. 11, 5616?5628] and some other papers.