On the best proximity point for the proximal contractive and nonexpansive mappings on the starshaped sets

Abstract

The purpose of this paper is to the best proximity point theorems for the proximal nonexpansive mapping on the starshaped sets by using a clever and simple method. The results improve and extend the recent results of Chen et al. (Fixed Point Theory Appl 2015:19, 2015). It should be noted that, the complex method is used by Jianren Chen et al. can be replaced by the clever and simple method presented in this paper.