A counterexample to the new iterative scheme of Rezapour et al.: Some discussions and corrections

Abstract

In this paper, we show a counterexample to the new iterative scheme introduced by Rezapour et al. in "A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems" [2]. We propose a modified iteration to conclude the convergence result. Moreover, some of our results are established under a weaker assumption.

Keywords

• common fixed point
• generalized α-nonexpansive mapping
• weak convergence
• strong convergence
• uniformly convex banach space
• strictly convex banach space