Compact Metric Space and Some Fixed-Point Theorems

The aim of this paper is to study some fixed point results in compact metric spaces. It discusses the existence and uniqueness of fixed point of a self-map on a metric space. In this paper we defined generalized contraction condition on the continuous self-mappings on compact metric spaces. Our result generalizes the results of Edelstein and Fisher. Keywords: Compact Space, Metric Space Contraction, Fixed Point, Convergence sequence