b-metric like spaces: A survey of concepts and applications

Introduction/Purpose: This paper presents a comprehensive survey of fixed-point results in metric-like spaces, with a particular emphasis on b-metric-like spaces. The purpose of the study was to explore the generalization of several important concepts in fixed point theory, including partial metric spaces, metric-like spaces, and b-metric spaces. This research aimed to contribute to the advancement of fixed-point theory in these generalized settings. Methods: The study involved reviewing foundational and recent research on fixed-point results in b-metric-like spaces. It focused on summarizing key contributions from the early stages of the field to the present, providing an extensive compilation of results. Additionally, the paper addressed open problems arising from the best proximity results in orthogonal 0-complete b-metric-like spaces. Results: The results highlighted significant contributions to the theory of fixed points in metric-like spaces, particularly in the context of b-metriclike spaces. The study offered affirmative answers to some open problems concerning the best proximity results in orthogonal 0-complete bmetric-like spaces, further enriching the theoretical framework. Conclusions: This paper is concluded by advancing the understanding of fixed point theory in generalized metric-like spaces. It provides researchers with valuable insights and references, which could facilitate further exploration and development in this field.