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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