Journal of Convex Analysis 33 (2026), No. 1&2, 543--560
Copyright Heldermann Verlag 2026
Dual Equilibrium Problems in Reflexive Banach Spaces
Monica Bianchi
Dip. di Matematica, Università Cattolica del Sacro Cuore, Milano, Italy
monica.bianchi@unicatt.it
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
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.
Keywords: Duality, equilibrium problems, Fenchel conjugation.
MSC: 49J40, 47H05, 47J20.
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