Strong convergence theorems based on a new modified extragradient method for variational inequality problems and fixed point problems in Banach spaces

Abstract

In this paper, we introduce a new iterative algorithm by a modified extragradient method for finding a common element of the set of solutions of a general variational inequality and the set of common fixed points of an infinite family of Ki-strict pseudocontractions in a Banach space. We obtain some strong convergence theorems under suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others. © 2011 Elsevier Ltd. All rights reserved.