Interpolative \(\alpha_{\mathfrak{p}}\)-contractions in \(C^*\)-algebra valued partial \(b\)-metric spaces: fixed point theorems and applications

Abstract

This study introduces interpolative contraction mappings in \(C^*\)-algebra valued partial \(b\)-metric spaces (\(C^*\)-avp\(b\)ms) through \(\alpha\)-admissible functions. We prove multiple coupled fixed point theorems for these contractions, supported by concrete examples. The theoretical developments find direct application in solving coupled Fredholm integral equations and analyzing homotopy continuation problems, demonstrating their utility in nonlinear analysis.