The Strict Feasibility Of Variational Inequality Problem

Recently, some researchers have studied the equivalence betweenstrict feasibility and solution set being nonempty and bounded for variationalinequality problem. In finite dimensional Euclidean spaces Rn, Pang[22,Theorem 2.4.4] proved that if K is a nonempty closed convex cone and themapping F is single-valued, continuous, and pseudomonotone on K, then thesolution set being nonempty and bounded is equivalent to the strict feasibility.In reffexive Banach space, He[23] proved that if K is a nonempty closedconvex subset and the set-mapping F is upper hemicontinuous and stablypseudomonotone on K, then the solution set being nonempty and bounded isequivalent to the strict feasibility.The main purpose of this paper is to generalize Theorem 2.4.4 in [22]from finite dimensional Euclidean spaces to infinite dimensional spaces, andrelax the stably pseudomonotonicity assumption of F in He[23] to F beingpseudomonotone.