Some results on a general iterative method for k-strictly pseudo-contractive mappings

Let H be a Hilbert space, C be a closed convex subset of H such that C +/- C subset of C, and T : C -> H be a k-strictly pseudo-contractive mapping with F(T) not equal empty set for some 0 <= k <1. Let F : C -> C be a kappa-Lipschitzian and eta-strongly monotone operator with kappa > 0 and eta > 0 and f : C -> C be a contraction with the contractive constant alpha is an element of (0, 1). Let 0 < mu < 2 eta/kappa(2), 0 < gamma < mu(eta-mu kappa(2)/2/alpha) = tau/alpha and tau < 1. Let {alpha(n)} and {beta(n)} be sequences in (0, 1). It is proved that under appropriate control conditions on {alpha n(}) and {beta(n)}, the sequence {x(n)} generated by the iterative scheme x(n+1) = alpha(n)gamma f(x(n)) + beta(n)x(n) + (( 1 - beta n)/-alpha(n)mu F)P(C)Sx(n), where S : C -> n is a mapping defined by Sx = kx + ( 1 - k)Tx and P-C is the metric projection of n onto C, converges strongly to q is an element of F(T), wnich solves the variational inequality <mu Fq - gamma f(q), q - p > <= 0 for p is an element of F(T).