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

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

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Article ID: iaor2014197
Volume: 160
Issue: 1
Start Page Number: 67
End Page Number: 89
Publication Date: Jan 2014
Journal: Journal of Optimization Theory and Applications
Authors: ,
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.

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