Abstract

Let ff be an equilibrium bifunction defined on the product space X×X\mathbb{X}\times\mathbb{X}, where X\mathbb{X} is a Banach space. If ff is locally Lipschitz with respect to the second variable, for every x∈Xx\in\mathbb{X} we define Tf(x)T_f(x) as the Clarke subdifferential of f(x,⋅)f(x,\cdot) evaluated at xx. This multivalued operator plays a fundamental role for the reformulation of equilibrium problems as variational inequality ones. We analyze additional conditions on ff which ensure the DD-maximal pseudomonotonicity and the cyclically pseudomonotonicity of TfT_f. Such results have consequences in terms of the characterization of the set of solutions of a subclass of pseudomonotone equilibrium problems.

Author information

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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

Keywords

  • Equilibrium problem
  • pseudomonotone bifunction
  • pseudomonotone operator
  • diagonal subdifferential

Mathematics Subject Classification

91B50, 47H05

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Suggested citation

M. Castellani, M. Giuli. “Pseudomonotone Diagonal Subdifferential Operators.” Journal of Convex Analysis 20 (2013), No. 1, 1–12. https://doi.org/10.68381/jca20001

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press.