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

Hristo S. Sendov and Ričardas Zitikis ()
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Hristo S. Sendov: University of Western Ontario
Ričardas Zitikis: University of Western Ontario

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 1, No 4, 67-89

Abstract: 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.

Keywords: Borwein–Affleck–Girgensohn function; Completely monotone function; Bernstein function; Harmonically convex function; Laplace transform; Quasi-arithmetic mean; Kolmogorov–Nagumo mean (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-013-0345-1

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