On the generalized C*- valued metric spaces related with Banach fixed point theory

Abstract

The Banach contraction principle, which shows that every contractive mapping has a unique fixed point in a complete metric space, has been extended in many directions. One of the branches of this theory is devoted to the study of fixed points. Especially, Fixed point theory in C*- algebra valued metric spaces has greatly developed in recent times. Also, we study on generalized C*- algebra valued metric space and give some examples, the idea of this metric is to replace the set of real numbers by the positive cone C*- algebras, the set of positive elements on the C*- algebras the notation introduced recently. Also, we prove certain fixed-point theorem for a single-valued mapping in such spaces. The mapping we consider here is assumed to satisfy certain D-metric conditions with generalized fixed-point theorem. Moreover, the paper provides an application to prove the existence and uniqueness of fixed points. (C) 2017 The Authors. Published by IASE.