Strong convergence for the modified Mann's iteration of λ-strict pseudocontraction

In this paper, for an lambda-strict pseudocontraction T, we prove strong convergence of the modified Mann's iteration defined by x(n+1) = beta(n)u + gamma(n)x(n) + (1 - beta(n) - gamma(n)) [alpha(n)Tx(n) + (1 - alpha(n))x(n)] where {alpha(n)}, {beta(n)} and {gamma(n)} in (0, 1) satisfy: ( i) 0 <= alpha(n) <= lambda/k(2) with lim inf(n ->infinity)alpha(n)(lambda - K-2 alpha(n)) > 0 ( ii) lim(n ->infinity)beta(n) = 0 and Sigma(infinity)(n-1)beta(n) = infinity; ( iii) lim sup(n ->infinity)gamma(n) < 1. Our results unify and improve some existing results. (C) 2014 Elsevier Inc. All rights reserved.