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Generalized variational-like inequalities with pseudomonotone set-valued mappings. (English) Zbl 1013.47026

Summary: In this paper, the authors introduce the concepts of \((\eta,h)\)-pseudo-monotone and \((\eta,h)\)-demi-monotone mappings and prove some existence results of solutions for a new class of generalized variational-like inequalities with pseudo-monotone set-valued mappings defined on noncompact sets in Hausdorff topological vector spaces.

MSC:

47J20 Variational and other types of inequalities involving nonlinear operators (general)
47H05 Monotone operators and generalizations
47H10 Fixed-point theorems
47H04 Set-valued operators
49J40 Variational inequalities
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