TITLE:
An Existence Theorem of Solutions for the System of Generalized Vector Quasi-Variational-Like Inequalities
AUTHORS:
Shamshad Husain, Sanjeev Gupta, Vishnu Narayan Mishra
KEYWORDS:
The System of Generalized Vector Quasi-Variational-Like Inequalities; Fixed Point Theorem; Open Lower Section; Upper Semicontinuous; C-Diagonal Quasiconvexity
JOURNAL NAME:
American Journal of Operations Research,
Vol.3 No.3,
May
23,
2013
ABSTRACT: 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.