Some fixed point and stability results in b-metric-like spaces with an application to integral equations on time scales

Abstract

This paper presents the stability theorem for the $ T $-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning $ T $-mean nonexpansive mappings within $ b $-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically.

Keywords

• stability
• fixed point
• $ b $-metric-like space
• $ t $-mean nonexpansive mapping
• hammerstein integral equation
• time scale