A Convex-Analytical Approach to Extension Results for n-Cyclically Monotone Operators

Results concerning extensions of monotone operators have a long history dating back to a classical paper by Debrunner and Flor from 1964. In 1999, Voisei obtained refinements of Debrunner and Flor’s work for n-cyclically monotone operators. His proofs rely on von Neumann’s minimax theorem as well as Kakutani’s fixed point theorem. In this note, we provide a new proof of the central case of Voisei’s work. This proof is more elementary and rooted in convex analysis. It utilizes only Fitzpatrick functions and Fenchel–Rockafellar duality.