Abstract
In this article, we prove the existence results of solutions for a new class of generalized quasi-variational-like inequalities (GQVLI) for η-h-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. In obtaining our results on GQVLI for η-h-pseudo-monotone type I operators, we use Chowdhury and Tan's generalized version of Ky Fan's minimax inequality as the main tool.
Highlights
If X is a nonempty set, we denote by 2X the family of all non-empty subsets of X and by F (x) the family of all non-empty finite subsets of X
Let s〈F, E〉 be the topology on F generated by the family {W (x; ∊) : x Î E, ∊ >0} as a subbase for the neighborhood system at 0 and δ〈F, E〉 be the topology on F generated by the family {U(A; ∊) : A is a non-empty bounded subset of E and ∊ >0} as a base for the neighborhood system at 0
Existence theorems for generalized quasi-variational-like inequalities for h-h-pseudo-monotone type I operators we prove some existence theorems for the solutions to the generalized quasi-variational-like inequalities for pseudo-monotone type I operators T with noncompact domain in locally convex Hausdorff topological vector spaces
Summary
If X is a nonempty set, we denote by 2X the family of all non-empty subsets of X and by F (x) the family of all non-empty finite subsets of X.
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