Strong convergence of implicit viscosity approximation methods for pseudocontractive mappings in Banach spaces

Let C be a nonempty closed convex subset of a uniformly smooth Banach space X. Let f : C -> C be a fixed contraction mapping, S : C -> C be a nonexpansive mapping and T : C -> C be a pseudocontractive mapping. Let {alpha(n)}, {beta(n)} and {gamma(n)} be three real sequences in (0, 1) such that alpha(n) + beta(n) + gamma(n) <= 1. For arbitrary x(0) is an element of C, the sequence {x(n)} is generated by x(n) = (1 - alpha(n) - beta(n) - gamma(n))x(n-1) + alpha(n)f(x(n-1)) + beta(n)Sx(n-1) + gamma(n)Tx(n) for all n >= 1. It is proven that under some conditions, {x(n)} converges strongly to a fixed point of T, which solves some variational inequality.