Generalized Vector Variational-Like Inequalities with Cx - η-Pseudomonotone Set-Valued Mappings

In this paper, we introduce and study a class of generalized vector variational-like inequalities involving C x - η-pseudomonotone and weakly C x - η-pseudomonotone set-valued mappings. The generalized vector variational-like inequality problem unifies and generalizes the generalized vector variational inequalities, vector variational inequalities and various extensions of the classic variational inequalities involving single-valued and set-valued mappings of various monotone types in the literature. Several existence theorems are established under noncompact setting in topological vector spaces. These new results unify and generalize many recent known results in the literature.

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