Convergence and certain control conditions for hybrid iterative algorithms

Abstract

Very recently, Yao et al. (2010) [4] proposed a hybrid iterative algorithm. Under the parameter sequences satisfying some quite restrictive conditions, they derived a strong convergence theorem in a Hilbert space. In this paper, under the weaker conditions, we prove the strong convergence of the sequence generated by their iterative algorithm to a common fixed point of an infinite family of nonexpansive mappings, which solves a variational inequality. An appropriate example, such that all conditions of this result that are satisfied and that other conditions are not satisfied, is provided. Moreover, the method of our paper is different from the method in Yao et al. (2010) [4].