Paul Carter, David Lowry-Duda
Published 2016-08-08Version 1
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 analogues and the existence of "weighted harmonic functions."
On functions whose mean value abscissas are Stolarsky means of endpoints
Deformations of singularities of meromorphic $\mathfrak{sl}_2(\mathbb{C})$-connections and meromorphic quadratic differentials
The Supremum Norm of the Discrepancy Function: Recent Results and Connections
![QR code for arXiv:1608.02558 [math.CA]](http://oss.arxitics.com/images/favicon.svg)