Abstract
A new notion of the A‐monotonicity is introduced, which generalizes the H‐monotonicity. Since the A‐monotonicity originates from hemivariational inequalities, and hemivariational inequalities are connected with nonconvex energy functions, it turns out to be a useful tool proving the existence of solutions of nonconvex constrained problems as well.
Highlights
A new notion of the A-monotonicity is introduced, which generalizes the H-monotonicity
Fang and Huang [1] introduced a new class of mappings—h-monotone mappings—in the context of solving a system of variational inclusions involving a combination of h-monotone and strongly monotone mappings based on the resolvent operator technique
We announce the notion of the A-monotone mappings and its applications to the solvability of systems of nonlinear variational inclusions
Summary
A new notion of the A-monotonicity is introduced, which generalizes the H-monotonicity. The notion of the h-monotonicity has revitalized the theory of maximal monotone mappings in several directions, especially in the domain of applications. We announce the notion of the A-monotone mappings and its applications to the solvability of systems of nonlinear variational inclusions.
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