• A STUDY OF FIXED POINT THEORY IN GENERALIZED b-METRIC SPACE

Abstract

Banach Contraction Principle (BCP), also known as Banach’s Fixed Point Theorem (BFT), concerns certain contraction mappings of a complete metric space into itself. It states sufficient conditions for the existence and uniqueness of a fixed point. The theorem also provides an iterative process from which we can obtain approximations to the fixed point along with error bounds.  In the study of fixed point theory, BCP has been extended and generalized in many different directions in usual metric spaces.  This work deals with the introduction of b-metric space and dislocated quasi b-metric space with some examples. Besides this, we also present some fixed point results on b-metric space and dislocated quasi b-metric space.