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Characterizations of r-Convex Functions

Author

Listed:
  • Y. X. Zhao

    (Chinese Academy of Sciences)

  • S. Y. Wang

    (Chinese Academy of Sciences)

  • L. Coladas Uria

    (Santiago de Compostela University)

Abstract

This paper discusses some properties of r-convexity and its relations with some other types of convexity. A characterization of convex functions in terms of r-convexity is given without assuming differentiability. The concept of strict r-convexity is introduced. For a twice continuously differentiable function f, it is shown that the strict r-convexity of f is equivalent to a certain condition on ∇ 2 f. Further, it is shown that this condition is satisfied by quasiconvex functions satisfying a less stringent condition.

Suggested Citation

  • Y. X. Zhao & S. Y. Wang & L. Coladas Uria, 2010. "Characterizations of r-Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 186-195, April.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:1:d:10.1007_s10957-009-9617-1
    DOI: 10.1007/s10957-009-9617-1
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    References listed on IDEAS

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    1. H. Z. Luo & Z. K. Xu, 2004. "On Characterizations of Prequasi-Invex Functions," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 429-439, February.
    2. X. M. Yang & X. Q. Yang & K. L. Teo, 2001. "Characterizations and Applications of Prequasi-Invex Functions," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 645-668, September.
    3. AVRIEL, Mordecai, 1973. "Solution of certain nonlinear programs involving r-convex functions," LIDAM Reprints CORE 129, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Rota-Graziosi, Grégoire, 2019. "The supermodularity of the tax competition game," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 25-35.
    2. Tamás L. Balogh & Christian Ewerhart, 2015. "On the origin of r-concavity and related concepts," ECON - Working Papers 187, Department of Economics - University of Zurich.
    3. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.

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