On a Generalization of Chatterjee's Fixed Point Theorem inb-metric Space

Abstract

Banach’s Fixed Point Theorem (BFT) deals with the certain contraction mappings of a complete metric space into itself. It states sufficient conditions for the existence and uniqueness of a fixed point. In the study of fixed point theory, BCP has been extended and generalized in many different directions in usual metric spaces. One of those generalizations is a b-metric space. Such generalizations have resulted in generalizing some popular metric fixed point theorems in the context of a b-metric space. In2013, Kir and Kiziltunc [8] attempted to generalize Chatterjee’s Fixed Point Theorem (CFPT) in the context of b-metric spaces. The proof of that generalization, however, had a minor flaw and an unstated assumption. This paper attempts to fix these issues by introducing new conditions. Keywords: Convergence, Compactness, Cauchy sequence, Metric space, b-Metric space.