G. Xiao, Z. Fan and X. Qi, “Existence Results for Generalized Nonlinear Vector Variational-Like Inequalities with Set-Valued Mapping,” Applied Mathematics Letter, Vol. 23, No. 1, 2010, pp. 44-47. doi:10.1016/j.aml.2009.07.023

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.