Strong convergence of an iterative algorithm for pseudocontractive mapping in Banach spaces

Abstract

Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X , T : C → C a pseudocontractive mapping. Let { α n } , { β n } and { γ n } be three real sequences in ( 0 , 1 ) satisfying appropriate conditions; then for fixed u ∈ C and arbitrary x 0 ∈ C , the sequence { x n } generated by x n = α n u + β n x n − 1 + γ n T x n , n ≥ 1 , converges strongly to a fixed point of T .