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The Shape of the Borwein–Affleck–Girgensohn Function Generated by Completely Monotone and Bernstein Functions

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  • Hristo S. Sendov

    (University of Western Ontario)

  • Ričardas Zitikis

    (University of Western Ontario)

Abstract

Fifteen years ago, J. Borwein, I. Affleck, and R. Girgensohn posed a problem concerning the shape (convexity, log-convexity, reciprocal concavity) of a certain function of several arguments that had manifested in a number of contexts concerned with optimization problems. In this paper we further explore the shape of the Borwein–Affleck–Girgensohn function as well as of its extensions generated by completely monotone and Bernstein functions.

Suggested Citation

  • Hristo S. Sendov & Ričardas Zitikis, 2014. "The Shape of the Borwein–Affleck–Girgensohn Function Generated by Completely Monotone and Bernstein Functions," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 67-89, January.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:1:d:10.1007_s10957-013-0345-1
    DOI: 10.1007/s10957-013-0345-1
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    References listed on IDEAS

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    1. Porcu, Emilio & Mateu, Jorge & Christakos, George, 2009. "Quasi-arithmetic means of covariance functions with potential applications to space-time data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1830-1844, September.
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    Cited by:

    1. Hristo Sendov & Shen Shan, 2015. "New Representation Theorems for Completely Monotone and Bernstein Functions with Convexity Properties on Their Measures," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1689-1725, December.
    2. Alexandru V. Asimit & Raluca Vernic & Ricardas Zitikis, 2016. "Background Risk Models and Stepwise Portfolio Construction," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 805-827, September.

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