International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 2, Pages 103-107
On a functional equation related to a generalization of Flett's mean value theorem
1Department of Mathematics, University of Louisville, Louisville 40292, KY, USA
2Instytut Matematyki, Uniwersytet Śląski, Ul. Bankowa 14, Katowice Pl-40-007, Poland
Received 24 November 1997; Revised 10 June 1998
Copyright © 2000 T. Riedel and Maciej Sablik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, we characterize all the functions that attain their
Flett mean value at a particular point between the endpoints of the
interval under consideration. These functions turn out to be cubic
polynomials and thus, we also characterize these.