Cone metric spaces and fixed point theorems of contractive mappings

Abstract

In this paper we introduce cone metric spaces, prove some fixed point theorems of contractive mappings on cone metric spaces.

In this paper, we replace the real numbers by ordering Banach space and define cone metric spaces (X, d ). We discuss some properties of convergence of sequences. We prove some fixed point theorems for contractive mappings. Our results generalized some fixed point theorems in metric spaces.