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

Amjad Ali; Muhammad Arshad; Eskandar Ameer; Asim Asiri; Amjad Ali; Muhammad Arshad; Eskandar Ameer; Asim Asiri

doi:10.3934/math.20231049

AIMS Mathematics

2023, Volume 8, Issue 9: 20576-20596. doi: 10.3934/math.20231049

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Research article

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

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

Received: 26 March 2023 Revised: 07 June 2023 Accepted: 12 June 2023 Published: 26 June 2023
MSC : 46T99, 47H10, 54H25

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.
- hybrid operators,
- fixed point,
- $ M $-dynamic iterative process $ M $ -metric space,
- multistage system,
- integral equation
Citation: Amjad Ali, Muhammad Arshad, Eskandar Ameer, Asim Asiri. Certain new iteration of hybrid operators with contractive $ M $ -dynamic relations[J]. AIMS Mathematics, 2023, 8(9): 20576-20596. doi: 10.3934/math.20231049

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Abstract

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.

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