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We consider a new system of generalized variational inequalities (SGVI) defined on two closed convex subsets of a real Hilbert space. To find the solution of considered SGVI, a parallel Mann iteration process and a parallel S-iteration process have been proposed and the strong convergence of the sequences generated by these parallel iteration processes is discussed. Numerical example illustrates that the proposed parallel S-iteration process has an advantage over parallel Mann iteration process in computing altering points of some mappings. [ABSTRACT FROM AUTHOR]

We study in this paper the existence and the approximation of solutions of variational inequalities involving generalized pseudocontractive mappings in Banach spaces. The convergence analysis of a proposed hybrid iterative method for approximating common zeros or fixed points of a possibly infinitely countable or uncountable family of such operators will be conducted within the conceptual framework of the "viscosity approximation technique" in reflexive Banach spaces with uniform Gâteaux differentiable norms. This technique should make existing or new results in solving variational inequalities more applicable. [ABSTRACT FROM AUTHOR]