On Fixed Point Theorems in Dislocated Quasi Metric Spaces

The aim of this paper is to establish new fixed point results for certain classes of mappings in the setting of dislocated quasi-metric (dq-metric) spaces by utilizing the concept of orbits around a point. The study focuses on relaxing the conventional completeness assumptions and instead applies orbital completeness, which provides a broader and more flexible framework for analysis. We extend and generalize existing fixed point theorems by considering various contractive conditions under orbital continuity. These generalizations contribute to the ongoing development of fixed point theory in non-symmetric spaces, such as dq-metric spaces, where the standard tools of metric space theory are not directly applicable. The results presented in this paper unify and improve previously known results and offer new insights into the structure of dislocated spaces. This work not only enhances the theoretical understanding of fixed points in generalized settings but also lays the groundwork for further applications in mathematical analysis and related disciplines.