Certain Applications via φ-Contraction Type Coupled Fixed Points in C^*-Algebra Valued S_b-Metric Spaces

Abstract

In this paper, we establish unique common coupled fixed-point findings for two pairs of ω-compatible mappings in C^*-algebra-valued S_b- metric spaces that meet φ-generalized contractive conditions. Also, we provide an example to back up the findings we were able to get. Additionally, the study offers an application to demonstrate homotopy and the existence and uniqueness of a solution for a non-linear integral problem.