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

Shamshad Husain, Sanjeev Gupta, Vishnu Narayan Mishra

Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, India.
Department of Applied Mathematics, Faculty of Engineering & Technology, Aligarh Muslim University, Aligarh, India.

DOI: 10.4236/ajor.2013.33029                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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