An Existence Theorem of Solutions for the System of Generalized Vector Quasi-Variational-Like Inequalities

• 作者: Sanjeev Gupta Shamshad Husain Vishnu Narayan Mishra
• 来源期刊: 美国运筹学期刊(英文)
• 学科: 数学
• 关键词: The System of Generalized VECTOR Quasi-Variational-Like INEQUALITIES Fixed Point Theorem Open Lower Section Upper SEMICONTINUOUS C-Diagonal Quasiconvexity
• 年，卷（期）: 2013,（3）
• 页码范围: 329-336
• 页数: 8页
• 分类号: O1

摘要

In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities, the system of vector variational-like inequalities, the system of vector quasi-variational inequalities, and several other systems as special cases. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the g-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for the system of generalized vector quasi-variational-like inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.