Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Journal of Convex Analysis 20 (2013), No. 1, 001--012Copyright 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 [Abstract-pdf] 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 [ Fulltext-pdf  (137  KB)] for subscribers only.