
Journal of Convex Analysis 20 (2013), No. 1, 001012 Copyright Heldermann Verlag 2013 Pseudomonotone Diagonal Subdifferential Operators Marco Castellani Dept. of Systems and Institutions for the Economy, University of L'Aquila, Via Giovanni Falcone 25, 67100 L'Aquila, Italy marco.castellani@univaq.it Massimiliano Giuli Dept. of Systems and Institutions for the Economy, University of L'Aquila, Via Giovanni Falcone 25, 67100 L'Aquila, Italy massimiliano.giuli@univaq.it [Abstractpdf] Let $f$ be an equilibrium bifunction defined on the product space $X\times X$, where $X$ is a Banach space. If $f$ is locally Lipschitz with respect to the second variable, for every $x\in X$ we define $T_f(x)$ as the Clarke subdifferential of $f(x,\cdot)$ evaluated at $x$. This multivalued operator plays a fundamental role for the reformulation of equilibrium problems as variational inequality ones. We analyze additional conditions on $f$ which ensure the $D$maximal pseudomonotonicity and the cyclically pseudomonotonicity of $T_f$. Such results have consequences in terms of the characterization of the set of solutions of a subclass of pseudomonotone equilibrium problems. Keywords: Equilibrium problem, pseudomonotone bifunction, pseudomonotone operator, diagonal subdifferential. MSC: 91B50, 47H05 [ Fulltextpdf (137 KB)] for subscribers only. 