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

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Author(s): Shamshad Husain | Sanjeev Gupta | Vishnu Narayan Mishra

Journal: American Journal of Operations Research
ISSN 2160-8830

Volume: 03;
Issue: 03;
Start page: 329;
Date: 2013;
Original page

Keywords: The System of Generalized Vector Quasi-Variational-Like Inequalities | Fixed Point Theorem | Open Lower Section | Upper Semicontinuous | C-Diagonal Quasiconvexity

ABSTRACT
In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalies 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.

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