GRAPHICAL VERSION OF BROUWER’S FIXED POINT THEOREMS OVER METRIC SPACE


By

By Kiran Dewangan 

Department of Mathematics, Government Dudhadhari Bajrang Girls Postgraduate Autonomous College, Raipur-492001 (Chhattisgarh), India Email: kirankumar250791@gmail.com, dewangan.kiran@gmail.com 

(Received: March 10, 2021; In format: June 06, 2021; Revised: March 15, 2024; Accepted: March 24, 2024) 


DOI: https://doi.org/10.58250/jnanabha.2024.54114 


 

Abstract

The aim of this paper is to present graphical version of Brouwer’s fixed point theorem and to establish some useful results of partial order set and nonexpansive mapping defined on a partial order set. One application of the fixed point theory by combining graph theory is discussed here by using Dijkstra’s algorithms which is useful in computer science. 


2020 Mathematical Sciences Classification: 47H09, 47H10 

Keywords and Phrases: Graphical metric space, Dijkstra’s algorithm, fixed point, edge-preserving mapping, nonexpansive mapping 

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