Certain new iteration of hybrid operators with contractive $ M $ -dynamic relations

Author:

Ali Amjad1,Arshad Muhammad1,Ameer Eskandar2,Asiri Asim3

Affiliation:

1. Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan

2. Department of Mathematics, Taiz University, Taiz, Yemen

3. Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Abstract

<abstract><p>This article investigates Wardowski's contraction in the setting of extended distance spaces known as $ M $-metric spaces using hybrid operators based an $ M $ -dynamic iterative process. The main purpose is to observe new set-valued Chatterjea type common fixed point theorems for hybrid operators with respect to an $ M $-dynamic iterative process, i.e., $ \check{D}(\Psi _{1}, \Psi _{2}, s_{0}) $. We realize an application: the existence of a solution for a multistage system and integral equation. Also, we give a graphical interpretation of our obtained theorems. The main results are explicated with the help of a relevant example. Some important corollaries are extracted from the main theorems as well.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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