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

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.

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*American Journal of Operations Research*, Vol. 3 No. 3, 2013, pp. 329-336. doi: 10.4236/ajor.2013.33029.

Conflicts of Interest

The authors declare no conflicts of interest.

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