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

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Abstract

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.

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Authors and Affiliations

  1. Mathematics, Irving K. Barber School, UBC Okanagan, Kelowna, British Columbia, V1V 1V7, Canada

    Heinz H. Bauschke & Xianfu Wang

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  1. Heinz H. Bauschke
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  2. Xianfu Wang
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Correspondence to Heinz H. Bauschke.

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Bauschke, H.H., Wang, X. A Convex-Analytical Approach to Extension Results for n-Cyclically Monotone Operators. Set-Valued Anal 15, 297–306 (2007). https://doi.org/10.1007/s11228-006-0029-1

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  • DOI: https://doi.org/10.1007/s11228-006-0029-1

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