Fixed Point Result on Generalized Cone b-Metric Spaces

Abstract

The purpose of this paper is to prove a fixed point result on contraction mapping in generalized cone b-metric space (in short GCbMS) as a generalization of cone metric space, cone b metric space and rectangular metric space. The conception of generalized metric space is a generalization of that of classical metric space. Several authors have proved fixed point theorems of contractive mappings on generalized metric spaces, which also generalized some corresponding fixed point results in classical metric spaces. In present paper, we prove a result that is extension of the Kannan fixed point theorem proved by Reny George <i>et al</i>. Our result is extend and unify several well known results in the literature available for cone and cone-b metric space.