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We consider the solvability of generalized variational inequalities involving multivalued relaxed monotone operators and single-valued nonexpansive mappings in the framework of Hilbert spaces. We also study the convergence criteria of iterative methods under some mild conditions. Our results improve and extend the recent ones announced by many others.

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings