Article citationsMore>>

Q. H. Ansari and J. C. Yao, “A Fixed Point Theorem and Its Applications to the System of varItional Ineqalities,” Bulletin of the Australian Mathematical Society, Vol. 59, No. 3, 1999, pp. 433-442. doi:10.1017/S0004972700033116

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.