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Generalized mildly nonconvex variational inequalities and its solvabilityKeywords: Generalized mildly variational inequalities , prox-regular sets , nonconvex sets , partially relaxed cocoercive operators , iterative method , convergence Abstract: Using the prox-regularity notion, we introduce and study a generalized mildly nonconvex variational inequality. We study existence and iterative approximation of its solution under the partially relaxed cocoercivity. Several consequences of the proposed nonconvex variational inequality are also discussed.
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