Nonlinear implicit variational inequalities involving partially relaxed pseudomonotone mappings

Based on a class of generalized iterative algorithms, approximation-solvability of a class of nonlinear implicit variational inequalities involving partially relaxed pseudomonotone mappings—a mild generalization of the general notion of partial relaxed monotonicity—is discussed. The partial relaxed monotonicity itself is a widely studied and computation-oriented class and is more general than the notions of cocoercivity and strong monotonicity.