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Summary: Ann. Sci. Math. Québec 21 (1997),no. 1,l-11.
EXTENDED GENERALIZED VECTOR VARIATIONAL-LIKE
INEQUALITIES FOR NONMONOTONE MULTIVALUED MAPS
QAMRULHASAN ANSAFU
RÉsuMÉ. Dansleprésenttravail,nousétudionsuneextensionduproblèmevectoriel
généralisé d'inéquationsde type variationnelet nous démontronsl'existencede sa
solutiondans le contexte des espaces vectoriels topologiques.Divers cas spéciaux
sont aussi traités.
ABSTRACT. In this paper, we study an extension of generalizedvector variational-
like inequality and prove the existence of its solution in the setting of Hausdorff
topologicalvector spaces. Severalspecialcases were also discussed.
1. Introduction. The vector variational inequality was introduced by Giannessi [8] in
the finite dimensional Euclidean space in 1980and has a lot of applications in vector
optimization, Since then it has been generalized in various directions. Ansari [il, Chen
et al. [2-61, Siddiqi et al. [12, 131,Lee et al. [il] and Yang [14] have studied vector
variational inequalities in abstract spaces. Variational inequalities and variational-like
inequalities for multivalued maps have been shown to be a useful tool in different
areas of optimization, optimal control, operations research and economics. Huang [9]
and Jou and Yao [101studied a more general form of generalized variational inequali-
ties. Recently, vector variational-like inequality for multivalued maps has been studied
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