Best Proximity Point for a New Class of Proximal Contraction

Abstract

Here, a new class of contraction namely generalized (a-u) h-f Geraghty proximal contraction is introduced. Then after, we proved a best proximity theorem in a complete metric space which ensure the existence of best proximity point for such contraction. Our result extends the best proximity point theorem obtained by Hamzehnejadi and Lashkaripour (Fixed Point theory and Applications, 2016) and other related fixed point theorems existing in the literature.