An Approximation of Solutions of Variational Inequalities
نویسنده
چکیده
It is known (see [5, 6]) that when K is a closed convex cone, problems NCP( f ,K) and VI( f ,K) are equivalent. To study the existence of solutions of the NCP( f ,K) and VI( f ,K) problems, many authors have used the techniques of KKM mappings, and the Fan-KKM theorem from fixed point theory (see [1, 5, 6, 7, 8, 9, 10]). In case B is a Hilbert space, Isac and other authors have used the notion of “exceptional family of elements” (EFE) and the LeraySchauder alternative theorem (see [5, 6]). In [1, 2], Alber generalized the metric projection operator PK to a generalized projection operator πK : B∗ → K from Hilbert spaces to uniformly convex and uniformly smooth Banach spaces and Alber used this operator to study VI( f ,K) problems and to
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