Abstract
In this paper, we introduce and study a new class of generalized nonlinear vector mixed quasi-variational-like inequalities governed by a multi-valued map in Hausdorff topological vector spaces which includes generalized vector mixed general quasi-variational-like inequalities, generalized nonlinear mixed variational-like inequalities, and so on. By using the fixed point theorem, we prove some existence theorems for the proposed inequality.
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, [ – ] and the references therein
A vector variational inequality in a finite-dimensional Euclidean space was first introduced by Giannessi [ ]
We consider a generalized nonlinear vector mixed quasi-variational-like inequality governed by a multi-valued map and establish some existence results in locally convex topological vector spaces by using the fixed point theorem
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, [ – ] and the references therein.
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