Abstract
In this paper, we define the concepts of (η,h)-quasi pseudo-monotone operators on compact set in locally convex Hausdorff topological vector spaces and prove the existence results of solutions for a class of generalized quasi variational type inequalities in locally convex Hausdorff topological vector spaces.
Highlights
Variational inequality theory has appeared as an effective and powerful tool to study and investigate a wide class of problems arising in pure and applied sciences including elasticity, optimization, economics, transportation, and structural analysis, see for instance [1,2]
We define the concepts of (η,h)-quasi pseudo-monotone operators on compact set in locally convex Hausdorff topological vector spaces and prove the existence results of solutions for a class of generalized quasi variational type inequalities in locally convex Hausdorff topological vector spaces
The pseudo-monotone type operators was first introduced in [5] with a slight variation in the name of this operator. Later these operators were renamed as pseudomonotone operators in [6]
Summary
Variational inequality theory has appeared as an effective and powerful tool to study and investigate a wide class of problems arising in pure and applied sciences including elasticity, optimization, economics, transportation, and structural analysis, see for instance [1,2]. Since Chen et al [4] have intensively studied vector variational inequalities in abstract spaces and have obtained existence theorems for their inequalities. The pseudo-monotone type operators was first introduced in [5] with a slight variation in the name of this operator. Later these operators were renamed as pseudomonotone operators in [6]. The pseudomonotone operators are set-valued generalization of the classical pseudomonotone operator with slight variations. In this paper we obtained some general theorems on solutions for a new class of generalized quasi variational type inequalities for (η,h)-quasi-pseudo-monotone operators defined as compact sets in topological vector spaces. There exists y K such that f x, y 0 for all x X
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