Novel fixed point theorems for orbital continuity in \(b\)-metric spaces: applications to integral equations and neural stability

Volume 41, Issue 1, pp 82--93 https://dx.doi.org/10.22436/jmcs.041.01.06

Publication Date: September 04, 2025 Submission Date: June 18, 2025 Revision Date: July 21, 2025 Accteptance Date: August 01, 2025

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Authors

G. M. Abd-Elhamed - Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia. - College of Girls, Ain Shams University, Egypt.

Abstract

This article establishes novel fixed point theorems for \(\Psi \)-orbitally continuous mappings in \(b\)-metric spaces, extending the foundational results. The findings are applied to demonstrate the existence and uniqueness solutions for nonlinear integral equations and analyzing the stability of neural networks.

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Keywords

• Orbitally continuous mappings
• nonlinear integral equations
• neural network
• \(b\)-metric spaces

MSC

•  37C25
•  54H25

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