Advancements in Fixed Point Results of Generalized Metric Spaces: A Survey

Abstract

The increasing significance of metric spaces and their applications in sciences and engineering has manifested over the years. This has led to the emergence of fixed point theory in metric spaces which in turn, has many practical usefulness in inequalities, approximation theory, optimization theory, image restoration and filtering, to mention but a few. Following up this development, in this paper, various results on G-metric spaces (also called generalized metric spaces) introduced by Mustafa and Sims are reviewed. Extensions of fixed point theorems for Lipschitzian-type mappings on G-metric spaces are compiled and a concise report on the transition in fixed point theorems on G-metric spaces are established. The aim of this survey is therefore, to examine and provide an up-to-date analysis of the important advancements in the fixed point theory of G-metric spaces. Consequently, this note is handy for researchers in the domain of metric and pseudo-metric spaces as they can easily appreciate how new results are delineated from the subsequent ones.