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Q. M. Liu, L. Y. Fan and G. H. Wang, “Generalized Vector Quasi-Equilibrium Problems with Set-Valued Mappings,” Applied Mathematics Letters, Vol. 21, No. 9, 2008, pp. 946-950. doi:10.1016/j.aml.2007.10.007

has been cited by the following article:

• 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.