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

Abstract

<abstract><p>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.</p></abstract>