From the text: “The purpose of this paper is to give some other alternate version of a result, concerning a variational inequality due to G. Allen [J. Math. Anal. Appl. 58, 1–10 (1977; Zbl 0383.49005)].
The following theorem is the main result of this paper.
Theorem. Let be a closed nonempty subset of a locally convex semi-reflexive topological vector space and let be a mapping such that:
(1) for each fixed , is weakly usc on .
(2) there exists a real such that
(i) for each and , the set is convex,
(ii) for each , ,
(iii) for a particular , the set is a bounded subset of .
Then there exists an such that for all ”.