Fixed Point Theorem on C ∗-algebra-valued Suprametric Spaces

C ∗-algebra valued Suprametric Spaces

Abstract

The present study’s objective is to propose a C∗-algebra-valued suprametric spaces to provide an appro priate generalization concerning both suprametric spaces and C ∗-algebra-valued metric spaces. The concepts of convergence, Cauchy sequence, and completeness are then examined through suprametric space with C ∗-algebra and illustrated with an example. Furthermore, the Banach fixed point theorem, established in pursuance of the same metric, is employed to determine the existence and uniqueness of the solution to an integral equation.