Abstract
In this paper, we generalize the concept of exceptional family of elements for a completely continuous field from Hilbert spaces to Banach spaces and we study the solvability of the variational inequalities with respect to a mapping f that is from a closed convex cone of a Banach space B to the dual space B ∗ by applying the generalized projection operator π K and by using the Leray–Schauder type alternative.
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