On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph

Abstract EN

We consider the problem of best proximity point in locally convex spaces endowed with a weakly convex digraph.

For that, we introduce the notions of nonself G-contraction and G-nonexpansive mappings, and we show that for each seminorm, we have a best proximity point.

In addition, we conclude our work with a result showing the existence of best proximity point for every seminorm.