Results pertaining to fixed points in ordered metric spaces with auxiliary functions and application to integral equation

Abstract

This paper delves into fixed point findings within a complete partially ordered $ b $-metric space, focusing on mappings that adhere to weakly contractive conditions in the presence of essential topological characteristics. These findings represent modifications of established results and further extend analogous outcomes in the existing literature. The conclusions are substantiated by illustrative examples that strengthen the conclusion of the paper.

Keywords

• weakly contractive conditions
• $ b $-metric space
• fixed point
• compatible mappings
• coincidence points
• coupled coincidence points