A note on 'A best proximity point theorem for Geraghty-contractions'

Abstract

In Caballero et al. (Fixed Point Theory Appl. (2012). doi:10.1186/1687- 1812-2012-231), the authors prove a best proximity point theorem for Geraghty nonself contraction. In this note, not only P-property has been weakened, but also an improved best proximity point theorem will be presented by a short and simple proof. An example which satisfies weak P-property but not P-property has been presented to demonstrate our results. © 2013 Zhang et al.; licensee Springer.