Functional Equations and the Cauchy Mean Value Theorem
arXiv:1508.00329
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.
14 pages, 3 figures