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arXiv · 2007.10153

On the Jensen convex and Jensen concave envelopes of means

Zsolt Páles·Paweł Pasteczka
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Abstract

In recent papers the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexity or concavity of a quasiarithmetic mean implies the the twice continuous differentiability of its generator. As a consequence of this result, we can characterize those quasiarithmetic means which admit a lower convex and upper concave quasiarithmetic envelop.

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BibTeXRIS

Zsolt Páles, Paweł Pasteczka. 2020-07-16. On the Jensen convex and Jensen concave envelopes of means. https://doi.org/10.1007/s00013-020-01544-2

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