International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 413-415

A note on a functional inequality

Horst Alzer

Department of Pure Mathematics, Applies Mathematics and Astronomy, University of South Africa, P.O. Box 392, Pretoria 0001, South Africa

Received 25 September 1990; Revised 5 March 1991

Copyright © 1992 Horst Alzer. 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.


We prove: If r1,,rk are (fixed) positive real numbers with j=1krj>1, then the only entire solutions φ: of the functional inequalityj=1k|φ(rjz)|(j=1krj)|φ(z)|kare φ(z)=czn, where c is a complex number and n is a positive integer.