Convergence theorems of a three-step iteration method for a countable family of pseudocontractive mappings

Abstract

Abstract The purpose of this paper is to construct a three-step iteration method (as follows) and obtain the convergence theorem for a countable family of Lipschitz pseudocontractive mappings in Hilbert space H. For the iteration format, { z n = ( 1 − γ n ) x n + γ n T n x n , y n = ( 1 − β n ) x n + β n T n z n , x n + 1 = ( 1 − α n ) x n + α n T n y n , under suitable conditions, we prove that the sequence { x n } generated from above converges strongly to a common fixed point of { T n } n ≥ 1 . The results obtained in this paper improve and extend previous results that have been proved for this class of nonlinear mappings. MSC:47H05, 47H09, 47H10.