STRONG CONVERGENCE THEOREMS FOR THREE-STEP ITERATIONS WITH ERRORS UNDER A MODIFIED SENTER AND DOTSON'S CONDITION

Abstract

Let C be a closed convex subset of a Banach space. In this paper, we construct a three-step iteration process {xn} with errors for three nonlinear mappings S, T, U : C → C given by: x1 ∈ C, zn = α nxn+β nU n xn+γ n wn ,y n = αnxn+βnT n zn+ γnvn ,x n+1 = αnxn + βnS n yn + γnun, for all n ≥ 1 and prove a strong convergence theorem under a modified Senter and Dotson's condition (A). This improves Xu and Noor's result in 2002. Further, we generalize a Khan and Fukhar-ud-dim's result in 2005.