Fixed Point Results for Multivalued Graphic Contractions in F-Metric Spaces

The present paper is devoted to the introduction and development of the notions of multivalued graphic contractions and multivalued GF-contractions in the setting of F-metric spaces. By extending the idea of contractions to multivalued mappings associated with an underlying graph structure, we aim to enrich the existing theory of fixed point results in generalized metric frameworks. The main contribution of this study is the establishment of new fixed point theorems for these classes of mappings in F-metric spaces, which provide a natural extension of classical fixed point principles. Furthermore, in order to demonstrate the validity and applicability of our theoretical findings, we construct a non-trivial illustrative example that highlights how the proposed conditions can be effectively utilized. These results not only advance the fixed point theory in abstract metric settings but also open potential avenues for applications in mathematical analysis and applied sciences.