Some Fixed Point Techniques using \(\psi\)-contraction Mapping on the \(\mathit{C}^*\)-algebra Valued Metric Space
Alshaimaa Awad *
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt.
Saleh Omran
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Fixed point theorems, \(\mathit{C}^*\)-algebra valued metric space, \(\psi\)-contraction mapping, system linear operator equation