• 제목/요약/키워드: generalized (${\psi}$, ${\theta}$, ${\varphi}$)-contraction

검색결과 2건 처리시간 0.017초

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

  • Handa, Amrish
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제26권3호
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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.

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.