Some fixed point theorems relating to the orbital continuity

Abstract

In this paper, we prove a fixed point theorem for asymptotically regular mappings on a metric space using orbital continuity of the selfmap. As an application of this result, a fixed point theorem is established in $T$-orbitally complete metric spaces. Our results extend Mukherjee's theorem [4] to $T$-orbitally complete metric spaces, and generalize the theorems of Jotic [5] and Neu{s}i'{c} [6].