A Literature Survey on Fixed-Point Results in Metric and Partial Order Metric Spaces

Maitreyee Dey

Abstract: The aim of this paper is to investigate some fixed- point results in metric space and partial order metric spaces. Fixed-point results for different types of contractive conditions are established, which generalize some existing fixed-point theorems.Partial b-metric spaces are characterized by a modified triangular inequality and that the self-distance of any point of space may notbe zero and the symmetry is preserved. The spaces with a symmetric property have interesting topological properties. Our results some fixed-point results in the context of metric spaces and partial order metric spaces can be deduced.

Keywords: Fixed-point theorem; Metric Space; Partial order metric space; Contraction mapping; Banach Space