Some Generalized Fixed Point Results on Compact Metric Spaces

Abstract

The goal of this research is to study some generalized fixed point results in compact metric space. It mainly focuses on the existence and unique fixed point of a selfmap on a compact metric space and its  generalizations. In this study iterative techniques due to Edelstein, Bhardwaj et al. and Sastry et al. are used to show existence of a unique fixed point for a selfmap satisfying certain generalized contractive conditions involving rational expressions. Examples are also provided in support of our results. Our results  generalize that of Edelstein and Fisher.

Key Words : Compact metric space, complete metric space, contractive map, contraction
map, iterative sequences, fixed point.