Abstract

The aim of this paper is to investigate the dual problem of a generalized equilibrium problem in the framework of a reflexive Banach space. By means of the Fenchel duality, we introduce the dual problem defined via the Fitzpatrick transform of the bifunction involved, that turns out to be an equilibrium problem itself in the dual space. We present conditions which entail the solvability of both primal and dual problems.

Author information

Contact details are reproduced from the original publication and may be historical.

Nicolas Hadjisavvas

University of the Aegean, Syros, Greece

nhad@aegean.gr

Rita Pini

Dip. di Matematica, Università degli Studi di Milano-Bicocca, Milano, Italy

rita.pini@unimib.it

Keywords

  • Duality
  • equilibrium problems
  • Fenchel conjugation

Mathematics Subject Classification

49J40, 47H05, 47J20

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Suggested citation

M. Bianchi, N. Hadjisavvas, R. Pini. “Dual Equilibrium Problems in Reflexive Banach Spaces.” Journal of Convex Analysis 33 (2026), No. 1&2, 543–560. https://doi.org/10.68381/jca33034

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.