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This article , X is a reflexive Banach space , K X is bounded , closed , convex subset . Our study contains (M) type operator variational inequality problem : ( ? ) F ∈ X *, seeking u ∈ K , so that ( w- f , v - u ) ≥ 0 , w ∈ Tu . Where T is a finite continuous , (M) type , bounded set value mapping . KKM mapping and Gwinner [1] of the theorem, we get the results of variational inequalities solvability . Concludes with a discussion of its application .
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