Coupled Fixed Point Theorems in Modular Metric Spaces Endowed with a Graph

Yogita Sharma; Shishir Jain

doi:10.5666/KMJ.2021.61.2.441

Article

Kyungpook Mathematical Journal 2021; 61(2): 441-453

Published online June 30, 2021

Coupled Fixed Point Theorems in Modular Metric Spaces Endowed with a Graph

Yogita Sharma^*, Shishir Jain

Department of Computer Science, Shri Vaishnav Institute of Management, Gumashta Nagar, Indore
e-mail : yogitasharma2006@gmail.com

Department of Mathematics, Shri Vaishnav Vidyapeeth Vishwavidyalaya, Gram Baroli, Sanwer Road, Indore
e-mail : jainshishir11@rediffmail.com

Received: March 25, 2020; Revised: September 19, 2020; Accepted: January 6, 2021

Abstract

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Abstract

In this work, we define the concept of a mixed G-monotone mapping on a modular metric space endowed with a graph, and prove some fixed point theorems for this new class of mappings. Results of this paper extend coupled fixed point theorems from partially ordered metric spaces into the modular metric spaces endowed with a graph. An example is presented to illustrate the new result.

Keywords: coupled fixed point, G-monotone mapping, connected graph, modular metric space, partial order relation