• Title/Summary/Keyword: weakly B-contraction

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SOME RESULTS ON BEST PROXIMITY POINT FOR CYCLIC B-CONTRACTION AND S-WEAKLY CYCLIC B-CONTRACTION MAPPINGS

  • V. Anbukkarasi ;R. Theivaraman;M. Marudai ;P. S. Srinivasan
    • The Pure and Applied Mathematics
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    • v.30 no.4
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    • pp.417-427
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    • 2023
  • The purpose of this paper is establish the existence of proximity point for the cyclic B-contraction mapping on metric spaces and uniformly convex Banach spaces. Also, we prove the common proximity point for the S-weakly cyclic B-contraction mapping. In addition, a few examples are provided to demonstrate our findings.

BEST PROXIMITY POINTS FOR CONTRACTIVE MAPPINGS IN GENERALIZED MODULAR METRIC SPACES

  • V. Anbukkarasi;M. Marudai;R. Theivaraman
    • Korean Journal of Mathematics
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    • v.31 no.2
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    • pp.123-131
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    • 2023
  • In this paper, we prove existence of best proximity points for 2-convex contraction, 2-sided contraction, and M-weakly cyclic 2-convex contraction mappings in the setting of complete strongly regular generalized modular metric spaces that generalize many results in the literature.

SOME FIXED POINT THEOREMS IN A GENERALIZED b2-METRIC SPACE OF (𝜓, 𝜑)-WEAKLY CONTRACTIVE MAPPINGS

  • Pravin Singh;Shivani Singh;Virath Singh
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.3
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    • pp.885-897
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    • 2024
  • The purpose of this paper is to introduce a class of distance altering functions that establish the existence and uniqueness of fixed points of 𝜈-admissible mappings that are subject to a generalized (𝜓, 𝜑)-almost weakly contraction on a generalized b2-metric space.

COMMON FIXED POINT RESULTS VIA F-CONTRACTION ON C* -ALGEBRA VALUED METRIC SPACES

  • Shivani Kukreti;Gopi Prasad;Ramesh Chandra Dimri
    • Korean Journal of Mathematics
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    • v.31 no.4
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    • pp.391-403
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    • 2023
  • In this work, we establish common fixed point results by utilizing a variant of F-contraction in the framework of C*-algebra valued metric spaces. We utilize E.A. and C.L.R. property possessed by the mappings to prove common fixed point results in the same metric settings. To validate the applicability of these common fixed point results, we provide illustrative examples too.

COMMON FIXED POINTS FOR WEAKENED COMPATIBLE MAPPINGS SATISFYING THE GENERALIZED ϕ-WEAK CONTRACTION CONDITION

  • Jain, Deepak;Kumar, Sanjay;Jung, Chahn Yong
    • The Pure and Applied Mathematics
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    • v.26 no.2
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    • pp.99-110
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    • 2019
  • In this paper, we prove some common fixed point theorems for pairs of weakened compatible mappings (subcompatible and occasionally weakly compatible mappings) satisfying a generalized ${\phi}-weak$ contraction condition involving various combinations of the metric functions. In fact, our results improve the results of Jain et al.. Also we provide an example for validity of our results.

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.

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

  • DESHPANDE, BHAVANA;HANDA, AMRISH
    • The Pure and Applied Mathematics
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    • v.22 no.3
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    • pp.199-214
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    • 2015
  • We establish a common coupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled oincidence point, we do not employ the condition of continuity of any mapping involved therein. An example is also given to validate our results. We improve, extend and generalize several known results.

TRIPLED FIXED POINT THEOREM FOR HYBRID PAIR OF MAPPINGS UNDER GENERALIZED NONLINEAR CONTRACTION

  • Deshpande, Bhavana;Sharma, Sushil;Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.21 no.1
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    • pp.23-38
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    • 2014
  • In this paper, we introduce the concept of w¡compatibility and weakly commutativity for hybrid pair of mappings $F:X{\times}X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$ and establish a common tripled fixed point theorem under generalized nonlinear contraction. An example is also given to validate our result. We improve, extend and generalize various known results.

COMMON COUPLED FIXED POINT RESULTS FOR HYBRID PAIR OF MAPPING UNDER GENERALIZED (𝜓, 𝜃, 𝜑)-CONTRACTION WITH APPLICATION

  • Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.26 no.3
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    • pp.111-131
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    • 2019
  • We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.