A Unified Hybrid Iterative Method for Solving Variational Inequalities Involving Generalized Pseudocontractive Mappings

We study in this paper the existence and approximation of solutions of variational inequalities involving generalized pseudo-contractive 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. This technique should make existing or new results in solving variational inequalities more applicable.