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On cyclic and \(n\)-cyclic monotonicity of bifunctions

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Abstract

In the recent literature, the connection between maximal monotone operators and the Fitzpatrick function is investigated. Subsequently, this relation has been extended to maximal monotone bifunctions and their Fitzpatrick transform. In this paper we generalize some of these results to maximal \(n\)-cyclically monotone and maximal cyclically monotone bifunctions, by introducing and studying the Fitzpatrick transforms of order \(n\) or infinite order for bifunctions.

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Correspondence to N. Hadjisavvas.

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Part of this work was done when the third author was visiting the Catholic University of Milan, Italy. The author wishes to thank the University for its hospitality.

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Alizadeh, M.H., Bianchi, M., Hadjisavvas, N. et al. On cyclic and \(n\)-cyclic monotonicity of bifunctions. J Glob Optim 60, 599–616 (2014). https://doi.org/10.1007/s10898-013-0113-7

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  • DOI: https://doi.org/10.1007/s10898-013-0113-7

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