Solving an integral equation via C ⋆ $\mathscr{C}^{\star}$ -algebra-valued partial b-metrics

Abstract

Abstract In this paper, we prove some common coupled fixed-point theorems on complete C ⋆ $\mathscr{C}^{\star}$ -algebra-valued partial b-metric spaces. Some of the well-known facts in the literature are generalized and expanded by the results shown. An example to illustrate our findings is presented. We also explore some of the applications of our key results.

Keywords

• Coupled coincidence point
• Coupled fixed point
• C ⋆ $\mathscr{C}^{\star}$ -algebra-valued partial b-metric space
• w-compatible