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In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse strongly monotone mapping. We prove a strong convergence theorem for the sequences generated by this scheme and give some applications of our convergence theorem. [ABSTRACT FROM AUTHOR]

It is well known that the rate of convergence of 5-iteration process introduced by Agarwal et al. [J. Nonlinear Convex Anal., 8 (1) (2007), 61-79.] is faster than Picard iteration process for contraction operators. Following the ideas of S-iteration process, we introduce a parallel S-iteration process for finding altering points of nonlinear operators. We apply our algorithms to solve a system of operator equations in Banach space setting. This work also includes convergence analysis of hybrid steepest-descent-like method and hybrid Newton-like method in the context of altering points. [ABSTRACT FROM AUTHOR]