Common Fixed Point And Best Approximation Results In Cone Metric Space

Abstract

Fixed point theory has many applications in different branches of science. This theory itself is a beautiful mixture of analysis, topology, and geometry. In 2007, Huang and Zhang introduced the concept of cone metric space as a generalization of metric space, in which they replace the set of real numbers with a real Banachspace. The concept of almost contraction for multi-valued mappings in the setting of cone metric spaces is defined and then we establish some fixed point and common fixed point results in the set-up of cone metric spaces. As an application, some invariant approximation results are obtained. The results of this paper extend and improve the
corresponding results of multi-valued mapping from metric space theory to cone metric spaces. The Authors proved several fixed point theorems for contractive type mappings on a cone metric space when the underlying cone is normal.