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EMPLOYING GENERALIZED (ψ,θ,φ)-CONTRACTION ON PARTIALLY ORDERED FUZZY METRIC SPACES WITH APPLICATIONS
Amrish Handa 한국수학교육학회 2020 純粹 및 應用數學 Vol.27 No.4
We establish fixed point and multidimensional fixed point results satis- fying 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 hypoth- esis. Our results generalize, extend and modify several well-known results in the literature.
UTILIZING GENERALIZED MEIR-KEELER CONTRACTION IN PERIODIC BOUNDARY VALUE PROBLEMS
( Amrish Handa ) 한국수학교육학회 2021 純粹 및 應用數學 Vol.28 No.4
This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir-Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. 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 some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.
Amrish Handa 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.4
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.
Multidimensional Coincidence Point Results for Contraction Mapping Principle
Amrish Handa 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.4
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.
Amrish Handa 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.3
We introduce (CLRg) property for hybrid pair F : X×X→2^X and g : X→X. We also introduce joint common limit range (JCLR) property for two hybrid pairs F,G : X×X→2^X and f, g : X→X. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (,,)-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.
EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED GERAGHTY-TYPE CONTRACTION WITH APPLICATION
Amrish Handa 한국수학교육학회 2020 純粹 및 應用數學 Vol.27 No.3
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.
APPLICATION OF CONTRACTION MAPPING PRINCIPLE IN PERIODIC BOUNDARY VALUE PROBLEMS
( Amrish Handa ) 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.3
We prove some common fixed point theorems for β-non-decreasing map-pings 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.
UTILIZING WEAK ψ-φ CONTRACTION ON FUZZY METRIC SPACES
( Amrish Handa ) 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.3
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.
Application of Contraction Mapping Principle in Integral Equation
Amrish Handa 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.4
In this manuscript, 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.
APPLICATION OF GENERALIZED WEAK CONTRACTION IN INTEGRAL EQUATION
( Amrish Handa ) 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.3
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.