Generalized vector complementarity-type problems in topological vector spaces

Authors:
Suhel A. Khan
Affiliations:
Department of Mathematics, BITS, Pilani-Dubai, Dubai International Academic City, Dubai, United Arab Emirates
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 3
Cited 1

Vector complementarity and minimal element problems

Journal of Optimization Theory and Applications
Vector Variational Inequalities with Semi-monotone Operators

Journal of Global Optimization
Topological Methods in Complementarity Theory (Nonconvex Optimization and Its Applications)

Topological Methods in Complementarity Theory (Nonconvex Optimization and Its Applications)

Generalized vector implicit quasi complementarity problems

Journal of Global Optimization

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Abstract

In this paper, we introduced the generalized vector variational inequality-type problem and the generalized vector complementarity-type problem in the setting of topological vector space. By utilizing a modified version of the Fan-KKM theorem, we investigated the nonemptyness and compactness of solution sets of these problems without the demipseudomonotonicity assumption. Further, we prove that solution sets of both the problems are equivalent to each other under some suitable conditions. The results of this paper generalize and improve several results that appeared recently in the literature.