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Fixed points of Kannan contractive mappings in relational metric spaces

Fixed points of Kannan contractive mappings in relational metric spaces In this paper, we prove an analogous version of fixed point theorem due to Kannan [Bull. Calcutta Math. Soc., 60, (1968), 71–76] via conditional contractive mappings and some other relational metrical notions. In the proof of present results, we utilize the notion of comparable mappings and some other well known classical fixed point theorems in the settings of relational and ordered metric spaces. We also, highlight the close connection of α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha $$\end{document}-admissible mappings with the binary relation and partial order relation as well. Radically, these investigations open another new direction of metric fixed point theory for contractive type mappings. Moreover, non-trivial examples are given to demonstrate the importance and usefulness of such findings. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

Fixed points of Kannan contractive mappings in relational metric spaces

Prasad, Gopi
The Journal of Analysis , Volume 29 (3) – Sep 1, 2021
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References (36)

Publisher
Springer Journals
Copyright
Copyright © Forum D'Analystes, Chennai 2020
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-020-00273-7
Publisher site
See Article on Publisher Site

Abstract

In this paper, we prove an analogous version of fixed point theorem due to Kannan [Bull. Calcutta Math. Soc., 60, (1968), 71–76] via conditional contractive mappings and some other relational metrical notions. In the proof of present results, we utilize the notion of comparable mappings and some other well known classical fixed point theorems in the settings of relational and ordered metric spaces. We also, highlight the close connection of α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha $$\end{document}-admissible mappings with the binary relation and partial order relation as well. Radically, these investigations open another new direction of metric fixed point theory for contractive type mappings. Moreover, non-trivial examples are given to demonstrate the importance and usefulness of such findings.

Journal

The Journal of Analysis – Springer Journals

Published: Sep 1, 2021

Keywords: Fixed point; R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}$$\end{document}-complete metric spaces; Kannan contractive mapping; 47H10; 54H25

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