• 제목/요약/키워드: g-non-decreasing mapping

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MULTIDIMENSIONAL COINCIDENCE POINT RESULTS FOR CONTRACTION MAPPING PRINCIPLE

  • Handa, Amrish
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제26권4호
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    • pp.277-288
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    • 2019
  • The main objective of this article is to establish some coincidence point theorem for g-non-decreasing mappings under contraction mapping principle on a partially ordered metric space. Furthermore, we constitute multidimensional results as a simple consequences of our unidimensional coincidence point theorem. Our results improve and generalize various known results.

EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED NONLINEAR CONTRACTION WITH APPLICATIONS

  • Deshpande, Bhavana;Handa, Amrish;Thoker, Shamim Ahmad
    • East Asian mathematical journal
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    • 제32권3호
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    • pp.333-354
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    • 2016
  • We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.

APPLICATION OF CONTRACTION MAPPING PRINCIPLE IN PERIODIC BOUNDARY VALUE PROBLEMS

  • Amrish Handa
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제30권3호
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    • pp.289-307
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    • 2023
  • We prove some common fixed point theorems for β-non-decreasing mappings under contraction mapping principle on partially ordered metric spaces. We study the existence of solution for periodic boundary value problems and also give an example to show the degree of validity of our hypothesis. Our results improve and generalize various known results.

NONLINEAR CONTRACTIONS IN PARTIALLY ORDERED QUASI b-METRIC SPACES

  • Shah, Masood Hussain;Hussain, Nawab
    • 대한수학회논문집
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    • 제27권1호
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    • pp.117-128
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    • 2012
  • Using the concept of a g-monotone mapping we prove some common fixed point theorems for g-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [Monotone generalized nonlinear contractions in partailly ordered metric spaces, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8].

APPLICATION OF CONTRACTION MAPPING PRINCIPLE IN INTEGRAL EQUATION

  • Amrish Handa
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제30권4호
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    • pp.443-461
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    • 2023
  • In this paper, we establish some common fixed point theorems satisfying contraction mapping principle on partially ordered non-Archimedean fuzzy metric spaces and also derive some coupled fixed point results with the help of established results. We investigate the solution of integral equation and also give an example to show the applicability of our results. These results generalize, improve and fuzzify several well-known results in the recent literature.

EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED GERAGHTY-TYPE CONTRACTION WITH APPLICATION

  • Handa, Amrish
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제27권3호
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    • pp.109-124
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    • 2020
  • We establish coincidence point theorem for S-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings F, G : X2 → X. As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

COINCIDENCE POINT RESULTS UNDER GERAGHTY-TYPE CONTRACTION

  • Amrish Handa
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제31권3호
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    • pp.325-336
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    • 2024
  • The main aim of this research article is to establish some coincidence point theorem for G-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. Furthermore, we derive some multidimensional results with the help of our unidimensional results. Our results improve and generalize various well-known results in the literature.

EMPLOYING GENERALIZED (𝜓, 𝜃, 𝜑)-CONTRACTION ON PARTIALLY ORDERED FUZZY METRIC SPACES WITH APPLICATIONS

  • Handa, Amrish
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제27권4호
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    • pp.207-229
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    • 2020
  • We establish fixed point and multidimensional fixed point results satisfying generalized (𝜓, 𝜃, 𝜑)-contraction on partially ordered non-Archimedean fuzzy metric spaces. By using this result we obtain the solution for periodic boundary value problems and give an example to show the degree of validity of our hypothesis. Our results generalize, extend and modify several well-known results in the literature.

UTILIZING ISOTONE MAPPINGS UNDER MIZOGUCHI-TAKAHASHI CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION

  • Handa, Amrish
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제26권4호
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    • pp.289-303
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    • 2019
  • We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Mizoguchi-Takahashi contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to integral equation. The results we obtain generalize, extend and unify several very recent related results in the literature.

UTILIZING ISOTONE MAPPINGS UNDER GERAGHTY-TYPE CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION

  • Deshpande, Bhavana;Handa, Amrish
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제25권4호
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    • pp.279-295
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    • 2018
  • We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Geraghty-type contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. Our results generalize, extend and unify several classical and very recent related results in the literature in metric spaces.