Fixed Point Theorem on Weak Contraction to Cone Metric Space

In this paper, the concept of metric space, replacing the set of real numbers by an ordered bench space and defined a cone metric space. The concept of weak contraction in Hilbert space was introduced by alter and guerre-delabriere and fixed point theorem was proved. Hoards has shown that the result of alter and guerre delabriere is valid in complete metric spaces also. The early growth of functional analysis was based on the nineteenth century function theory and was given a great impetus by the birth of lebesgue theory of measure and integration. Functional analysis is the study of certain topological-algebraic structures and of the methods by which knowledge of these structures can be applied to analytic problems. We state the result of hoards below. We remove the restriction of continuity on. Supporting examples are also provided. Two open problems are given at the end.