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.
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Dedicated to Professor Jürg Rätz
The authors were supported by the Swiss National Science Foundation, SNF, Grant No. 200020 146477.
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Balogh, Z.M., Ibrogimov, O.O. & Mityagin, B.S. Functional equations and the Cauchy mean value theorem. Aequat. Math. 90, 683–697 (2016). https://doi.org/10.1007/s00010-015-0395-6
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DOI: https://doi.org/10.1007/s00010-015-0395-6