BEST PROXIMITY POINTS FOR WEAK PROXIMAL ENRICHED <i>G</i>-CONTRACTIONS IN GRAPHICAL CONVEX METRIC SPACES

In this paper, we redefine the concept of a graphical convex metric space involving sets with a graphical structure, and a new class of non-self mappings, called weak proximal enriched $ G- $contractions, is introduced in the aforementioned space. Moreover, we demonstrate the existence of best approximation points for two types of weak proximal enriched $ G- $contractions in graphical convex metric spaces, under suitable control conditions. Additionally, we provide examples to confirm our main results.