Common Fixed Point and Best Proximity Point Theorems in C*-Algebra-Valued Metric Spaces

Abstract

In the article, we prove the existence and uniqueness of common fixed points for self-maps with contractive or expansive conditions on C * -algebra-valued metric spaces without taking the continuity assumption on either of the mappings S or T . Also, we define C * -algebravalued proximal contraction and show the existence and uniqueness of best proximity points for these proximal contraction mappings on the said spaces. Moreover, the paper provides an application to prove the existence and uniqueness of the solution for a type of integral equations.