Year: 2022
Author: Gopi Prasad, Ramesh Chandra Dimri
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 2 : pp. 232–242
Abstract
In this paper, we prove fixed point theorem for weakly contractive mappings using locally $T$-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions. Our fixed point results under universal relation reduces to Harjani and Sadarangani [Nonlinear Anal., 71 (2009), 3403–3410] fixed point theorems. In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2017-0044
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 2 : pp. 232–242
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: $\mathcal{R}$-continuity locally $T$-transitive binary relation weakly contractive map.