Iterative Methods for Pseudocontractive Mappings in Banach Spaces

Let E a reflexive Banach space having a uniformly Gateaux differentiable norm. Let C be a nonempty closed convex subset of E, T : C -> C a continuous pseudocontractive mapping with F(T) not equal empty set, and A : C -> C a continuous bounded strongly pseudocontractive mapping with a pseudocontractive constant k is an element of (0,1). Let {alpha(n)} and {beta(n)} be sequences in (0, 1) satisfying suitable conditions and for arbitrary initial value x(0) is an element of C, let the sequence {x(n)} be generated by x(n) = alpha(n)Ax(n) + beta(n)x(n-1) +(1-alpha(n)-beta(n))Tx(n), n >= 1. If either every weakly compact convex subset of E has the fixed point property for nonexpansive mappings or E is strictly convex, then {x(n)} converges strongly to a fixed point of T, which solves a certain variational inequality related to A.