Add to ORKGWe introduce and study a new class of generalized nonlinear mixed variational-like in-equalities in reflexive Banach spaces. By applying Ding’s technique we prove several ex-istence and uniqueness theorems of solutions for the generalized nonlinear mixed varia-tional-like inequality, extend the auxiliary problem technique to suggest and analyze an it-erative method to compute the approximate solutions of the generalized nonlinear mixed variational-like inequality, and establish the convergence criteria of the iterative method. The results presented in this paper improve, extend, and unify many known results in this area. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1
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