Certain Applications of \(\left(\psi, \phi\right)\)-Contractions in \(C^*\)-Algebra-Valued \(S_b\)-Metric Spaces

We present in this paper unique common coupled fixed-point results for two pairs of ω-compatible mappings that satisfy (ψ, φ)-generalized weakly contractive conditions in C∗-algebra-valued Sb -metric spaces. Additionally, we provide an illustration to substantiate our findings. Additionally, the paper offers an application that demonstrates the existence and uniqueness of a solution for a non-linear integral equation, as well as homotopy.