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On Second-Order Generalized Convexity

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Abstract

Second-order convex functions were introduced by Mond (Opsearch 11(2–3):90–99, 1974) in order to deal with second-order duality. Then that notion was generalized again and again, using more and more parameters introduced using several quantifiers. In the present paper, we show that most of these notions have quite simple intrinsic characterizations. This paper can be viewed as a continuation of our paper (Zălinescu in An Ştiinţ Univ Al I Cuza Iaşi Secţ I a Mat 35(3):213–220, 1989) in which we characterized generalized bonvex functions.

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Acknowledgments

We thank Prof. M. Durea for his remarks on a previous version of the manuscript. This research was supported by the Grant PN-II-ID-PCE-2011-3-0084, CNCS-UEFISCDI, Romania.

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  1. Faculty of Mathematics, University Alexandru Ioan Cuza, 700506, Iasi, Romania

    C. Zălinescu

  2. Octav Mayer Institute of Mathematics, Romanian Academy, Iasi, Romania

    C. Zălinescu

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  1. C. Zălinescu
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Correspondence to C. Zălinescu.

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Zălinescu, C. On Second-Order Generalized Convexity. J Optim Theory Appl 168, 802–829 (2016). https://doi.org/10.1007/s10957-015-0820-y

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