Summary: Ann. Sci.Math. Québec 19 (1995),no. 2, 131-137.
ON GENERALIZED VECTOR VARIATIONAL-LIKE INEQUALITIES
RÉsud. Dans le présentarticlenous introduisonsle problèmevectorielgénéralisé
d'inéquationvariationnelleet établissonsl'existencede sa solutiondansle contexte
des espacesde Banachréflexifs.Plusieurscas spéciauxsont aussi considérés.
ABSTRACT.In this paper, we introduce the generalized vector variational-likein-
equality and prove the existenceof its solution in the setting of reflexive Banach
spaces. Several specialcases were also discussed.
1.Introduction. Because of the applicationsin different areas of optimization,optimal
control, operations Research and economics, the vector variational inequality, which
was introduced by Giannessi  in the finite dimensional Euclidean space in 1980,has
been generalized in various directions. Since then Chen et al. [l-51,Siddiqi et al. [lO,
113,Lee et al. [SI and Yang  have studied vector variational inequalities in abstract
spaces. Siddiqi, Ansari and Ahmad [lO]introduced and studied vector variational-like
inequalities in reflexive Banach spaces and topological vector spaces. In 1990, Chen
and Craven  introduced and studied vector variational inequalities for multivalued
mappings which are called generalized vector variational inequalities. Recently, Lee et
al. [SIstudied generalized vector variational inequalities in reflexive Banach spaces.
In this paper, we introduce a more general form of vector variational inequality