
Journal of Convex Analysis 16 (2009), No. 3, 807826 Copyright Heldermann Verlag 2009 An Existence Result for Equilibrium Problems with Some Surjectivity Consequences Alfredo N. Iusem Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, CEP 22460320 Rio de Janeiro, Brazil iusp@impa.br Gábor Kassay Faculty of Mathematics and Computer Sciences, BabesBolyai University, 1 Kogalniceanu Street, 400084 ClujNapoca, Romania kassay@math.ubbcluj.ro Wilfredo Sosa Universidad Nacional de Ingeniería, Instituto de Matemática y Ciencias Afines, Calle de los Biólogos 245, Lima 12, Perú sosa@uni.edu.pe We present conditions for existence of solutions of equilibrium problems, which are sufficient in finite dimensional spaces, without making any monotonicity assumption on the bifunction which defines the problem. As a consequence we establish surjectivity of setvalued operators of the form T + λI, with λ > 0, where T satisfies a property weaker than monotonicity, which we call premonotonicity. We study next the notion of maximal premonotonicity. Finally we adapt our condition for nonconvex optimization problems, obtaining as a byproduct an alternative proof of FrankWolfe's Theorem. Keywords: Equilibrium problems, convex feasibility problems, variational inequalities, convex optimization. MSC: 90C47, 49J35 [ Fulltextpdf (187 KB)] for subscribers only. 