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Vol.31 No.3

A. Herminau Jothy(Bharathidasan University) ; P. S. SRINIVASAN(BHARATHIDASAN UNIVERSITY) ; R. Theivaraman(BHARATHIDASAN UNIVERSITY) pp.251-265 https://doi.org/10.7468/jksmeb.2024.31.3.251
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Abstract

The main aim of this article is to present new fixed point results concerning existence of selection for a multivalued map on hyperconvex product space taking values on bounded, externally hyperconvex subsets under some appropriate hypothesis. Our results are significant extensions of some pioneering results in the literature, in particular M. A. Khamsi, W. A. Krik and Carlos Martinez Yanez, have proved the existence of single valued selection of a lipschitzian multi-valued map on hyperconvex space. Some suitable examples are also given to support and understand the applicability of our results.

Shivani Kukreti(HNB Garhwal University) ; Gopi Prasad(Government Degree College Rudraprayag) ; Ramesh Chandra Dimri(HNB Garhwal University) pp.267-281 https://doi.org/10.7468/jksmeb.2024.31.3.267
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Abstract

Aim is to present fixed point theorems for contractive mappings in the settings of partial metric spaces equipped with graph. To substantiate the claims and importance of newly obtained fixed point results, we present an application and non-trivial examples. In the light of an application, we ensure the existence of a solution of the linear integral equation via fixed point results. In this way, we generalize, extend and modify some important recent fixed point results of the existing literature, that is, in the settings of partial metric spaces equipped with graph.

Ghorban Khalilzadeh Ranjbar(Bu-Ali Sina University) pp.283-298 https://doi.org/10.7468/jksmeb.2024.31.3.283
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Abstract

In this paper, by using fixed point techniques, we establish some common fixed point theorems for mappings satisfying an α-ψ-φ-contractive condition in generalized tripled metric space. Finally, we give an example to illustrate our main outcome.

Sarmila Bhattacharyya(Netaji Mahavidyalaya) ; Tanmay Biswas ; Chinmay Biswas(Nabadwip Vidyasagar College) pp.299-310 https://doi.org/10.7468/jksmeb.2024.31.3.299
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Abstract

The probabilistic metric space as one of the important generalizations of metric space, was introduced by Menger [16] in 1942. Later, Choi et al. [6] initiated the notion of bicomplex-valued metric spaces (bi-CVMS). Recently, Bhattacharyya et al. [3] linked the concept of bicomplex-valued metric spaces and menger spaces, and initiated menger space with bicomplex-valued metric. Here, in this paper, we have taken probabilistic metric space with bicomplex-valued metric, i.e., bicomplexvalued probabilistic metric space and proved some common fixed point theorems using converse commuting mappings in this space.

Hüseyin Budak(Düzce University) ; Umut Baş(Kahramanmaraş Sütccü Imam University) ; Hasan Kara(Duzce University) ; Mohammad Esmael Samei(Bu-Ali Sina University) pp.311-324 https://doi.org/10.7468/jksmeb.2024.31.3.311
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Abstract

This article presents the above and below bounds for Midpoint and Trapezoid types inequalities for ψ-Hilfer fractional integrals with the assistance of the functions whose second derivatives are bounded. We also possess some extensions and generalizations of Hermite–Hadamard inequalities via ψ-Hilfer fractional integrals with the aid of the functions that have the conditions that will said.

Amrish Handa(Govt. P. G. Arts and Science College) pp.325-336 https://doi.org/10.7468/jksmeb.2024.31.3.325
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Abstract

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.

Shilpa Rahurikar(Shri Vaishnav Vidyapeeth Vishwavidyalaya) ; Varsha Pathak(Shri Vaishnav Vidyapeeth Vishwavidyalaya) ; Satish Shukla(Shri Vaishnav Vidyapeeth Vishwavidyalaya) pp.337-354 https://doi.org/10.7468/jksmeb.2024.31.3.337
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Abstract

In this paper, some best proximity points results for ψ-φ-contractions on complete metric spaces are proved. These results extend and generalize some best proximity and fixed point results on complete metric spaces. An example and some corollaries are provided that demonstrate the results proved herein.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics