Abstract
The aim of this paper is to describe the solution (f, g) of the equation
where \(I\subset \mathbb {R}\) is an open interval, \(f,g:I\rightarrow \mathbb {R}\) are differentiable, \(\alpha \) is a fixed number from (0, 1).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aczél, J.: A mean value property of the derivative of quadratic polynomials-without mean values and derivatives. Math. Mag. 58(1), 42–45 (1985)
Balogh, Z.M., Ibrogimov, O.O., Mityagin, B.S.: Functional equations and the Cauchy mean value theorem. Aequ. Math. 90, 683–697 (2016)
Haruki, S.: A property of quadratic polynomials. Am. Math. Monthly 86(7), 577–579 (1979)
Lundberg, A.: A rational Sûto equation. Aequ. Math. 57, 254–277 (1999)
Lundberg, A.: Sequential derivatives and their application to a Sûto equation. Aequ. Math. 61, 48–59 (2001)
Sahoo, P.K., Riedel, T.: Mean Value Theorems and Functional Equations. World Scientific Publishing Co., Inc., River Edge (1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Łukasik, R. A note on functional equations connected with the Cauchy mean value theorem. Aequat. Math. 92, 935–947 (2018). https://doi.org/10.1007/s00010-018-0583-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-018-0583-2