Graph-Theoretic Perspectives on Fixed Points in Double-Composed Metric Spaces

This study explores the development of fixed-point results in the setting of the recently proposed double-composed metric spaces. We establish conditions ensuring both existence and uniqueness of fixed points for several types of contractive mappings defined on such spaces. To enrich the analysis, the space is further equipped with a graph structure through the use of concepts from graph theory, leading to the formulation of two novel fixed-point theorems. An illustrative example is also provided to highlight the applicability and relevance of the obtained results.