NEW CONTRIBUTION IN BEST PROXIMITY POINT THEORY VIA AN AUXILIARY FUNCTION

Abstract

In this thesis, we introduce the notion of proximal τ -distance contraction, proximal contractive and proximal T -contractive mappings. We establish best proximity point theorems, there by extending fixed point theory to the case of non self mapping and we prove the existence and uniqueness of a best proximity point for such types of mappings in a Hausdorff topological space. Examples are given to validate the main results.