Fixed Point Theorems in Dislocated Quasi Metric and Dislocated Quasi b-Metric Spaces

Abstract

In this paper, the concept of generalized contraction mapping has been used in investigating fixed point theorems. A fixed point theorem of integral type will be establish in the setting of dislocated quasi metric spaces using some new type of rational contraction conditions. Moreover, a fixed point theorem will be studied in the context of dislocated quasi b-metric spaces using the idea of generalized new contraction conditions. Several corollaries may be deduced from our established results, which generalize and extend several results of the literature. Also , our investigated results may be easily used in solving equations in non-linear analysis too.