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 like 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 orbitally continuous boundedly compact and T-orbitally compact metric spaces. 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 in strengthening the hypotheses of our proved theorems.