On fixed points of generalized Kannan and Reich type contractive mappings

Abstract

Kannan or Reich type strict contractive conditions do not ensure the existence of fixed points unless some strong conditions such as compactness of the space and continuity of the mapping are assumed. In this paper, our main aim is to investigate the existence of fixed point of generalized Kannan type contractive mappings in the setting of boundedly compact and T-orbitally compact metric spaces via orbital continuity. In addition to it, asymptotic regularity has been used to prove the Reich type fixed point theorem via altering distance functions. Supporting examples have been given to strengthen the hypotheses of our proved theorems.