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An Existence Theorem of Solutions for the System of Generalized Vector Quasi-Variational-Like Inequalities
Department of Applied Mathematics, Faculty of Engineering & Technology, Aligarh Muslim University, Aligarh, India
Department of Applied Mathematics, Faculty of Engineering & Technology, Aligarh Muslim University, Aligarh, India
Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, India
- 1 Department of Applied Mathematics, Faculty of Engineering & Technology, Aligarh Muslim University, Aligarh, India
- 2 Department of Applied Mathematics, Faculty of Engineering & Technology, Aligarh Muslim University, Aligarh, India
- 3 Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, India
American Journal of Operations Research·Volume 03 (2013)·Pages 329–336·Published 23 May 2013·DOI10.4236/ajor.2013.33029
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Abstract
In this paper, we introduce and study the system of generalized vector quasi-variational-like inequali ti es 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 generaliz a tions of several known results in the literature.
KeywordsThe System of Generalized Vector Quasi-Variational-Like InequalitiesFixed Point TheoremOpen Lower SectionUpper SemicontinuousC-Diagonal Quasiconvexity
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