A remark on the paper “A note on the paper Best proximity point results for p-proximal contractions”

Abstract

Recently, Altun et al. [1] introduced the notion of p-proximal contractions and discussed about best proximity point results for this class of mappings. Then Gabeleh and Markin [4] showed that the best proximity point theorem proved by Altun et al. in [1] follows from the fixed point theory. In this short note, we show that if the p-proximal contraction constant \(k<\frac{1}{3}\) then the existence of best proximity point for p-proximal contractions follows from the celebrated Banach contraction principle.