Functional Equations and the Cauchy Mean Value Theorem
Classical Analysis and ODEs
2015-08-04 v1
Abstract
The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy Mean Value Theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.
Cite
@article{arxiv.1508.00329,
title = {Functional Equations and the Cauchy Mean Value Theorem},
author = {Zoltan M. Balogh and Orif O. Ibrogimov and Boris S. Mityagin},
journal= {arXiv preprint arXiv:1508.00329},
year = {2015}
}
Comments
14 pages, 3 figures