Solution of a Fredholm integral equation on \(C^\star \)-algebra-valued partial b-metric spaces

Abstract

In this paper, we prove fixed point theorems for generalized contraction on complete \(C^\star \)-algebra-valued partial b-metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by the obtained results. An instance to help our outcome is presented. We also explore some of applications of our key results.