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arXiv · 1710.01108

Interval-type theorems concerning quasi-arithmetic means

Paweł Pasteczka
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Abstract

Family of quasi-arithmetic means has a natural, partial order (point-wise order) $A^{[f]}\le A^{[g]}$ if and only if $A^{[f]}(v)\le A^{[g]}(v)$ for all admissible vectors $v$ ($f,\,g$ and, later, $h$ are continuous and monotone and defined on a common interval). Therefore one can introduce the notion of interval-type sets (sets $\mathcal{I}$ such that whenever $A^{[f]} \le A^{[h]} \le A^{[g]}$ for some $A^{[f]},\,A^{[g]} \in \mathcal{I}$ then $A^{[h]} \in \mathcal{I}$ too). Our aim is to give examples of interval-type sets involving vary smoothness assumptions of generating functions.

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Paweł Pasteczka. 2017-10-03. Interval-type theorems concerning quasi-arithmetic means. https://doi.org/10.7153/mia-2019-22-35

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