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http://dx.doi.org/10.7468/jksmeb.2021.28.3.253

FIXED POINTS OF SET-VALUED MAPPINGS IN RELATIONAL METRIC SPACES  

Prasad, Gopi (Department of Mathematics, HNB Garhwal University)
Dimri, Ramesh Chandra (Department of Mathematics, HNB Garhwal University)
Kukreti, Shivani (Department of Mathematics, HNB Garhwal University)
Publication Information
The Pure and Applied Mathematics / v.28, no.3, 2021 , pp. 253-266 More about this Journal
Abstract
In this paper, we generalize the notion of comparable set-valued mappings by introducing two types of 𝓡-closed set-valued mappings and utilize these to obtain an analogue of celebrated Mizoguchi and Takahashi fixed point theorem in relational metric spaces. To annotate the claims and usefulness of such findings, we prove fixed point results for both set-valued and single-valued mappings and validate the assertions with the help of examples. In this way, these investigations extend, modify and generalize some prominent recent fixed point results obtained by Tiammee and Suantai [24], Amini-Harandi and Emami [4], Prasad and Dimri [19] and several others in the settings of relational metric spaces.
Keywords
fixed point; ${\mathcal{R}}$-complete metric spaces; ${\mathcal{R}}$-closed set-valued mappings;
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