A fixed point theorem for \(G_f\)-Kannan contractive mappings in generalized suprametric spaces with a digraph

Abstract

In this paper, we introduce a fixed point theorem for a new class of \(G_f\)-Kannan contractive mappings defined on generalized suprametric spaces with a reflexive digraph. Although various extensions of Kannan’s fixed point theorem have been studied in many generalized metric spaces, few results address the interaction between contractive conditions and additional relational structures, such as digraphs. Our approach incorporates the structure of a digraph into the analysis considering the connectivity between points, allowing us to generalize existing theorems and unify different frameworks. We prove the uniqueness of fixed points under suitable conditions and provide a nontrivial example to illustrate the applicability of our result. This work contributes to the ongoing development of fixed point theory in generalized suprametric spaces and opens new directions for research involving relational structures defined by graphs.