On functions whose mean value abscissas are midpoints, with connections to harmonic functions

Paul Carter, David Lowry-Duda

Research output: Contribution to journalArticle

Abstract

We investigate functions with the property that for every interval, the slope at the midpoint of the interval is the same as the average slope. More generally, we find functions whose average slopes over intervals are given by the slope at a weighted average of the endpoints of those intervals. This is equivalent to finding functions satisfying a weighted mean value property. In the course of our exploration, we find connections to harmonic functions that prompt us to explore multivariable analogs and the existence of "weighted harmonic functions".

Original languageEnglish (US)
Pages (from-to)535-542
Number of pages8
JournalAmerican Mathematical Monthly
Volume124
Issue number6
DOIs
StatePublished - Jun 1 2017
Externally publishedYes

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