Some Fixed Point Techniques using \(\psi\)-contraction Mapping on the \(\mathit{C}^*\)-algebra Valued Metric Space

In this article, we introduced and focused our attention to some fixed point theorems using \(\psi\)-contraction mapping on \(\mathit{C}^*\)-algebra valued metric space. In particular, we established some Banach fixed point theorem as well as several extensions and generalizations of this theorem in \(\mathit{C}^*\)-algebras valued metric spaces. Moreover, in order to illustrate the current results, some basic examples are presented and we gave an application on system linear operator equation by investigating the existence and uniqueness to the solution of this equation.