International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 413-415
doi:10.1155/S0161171292000553
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
Abstract
We prove: If r1,…,rk are (fixed) positive real numbers with ∏j=1krj>1, then the only entire solutions φ:ℂ→ℂ of the functional inequality∏j=1k|φ(rjz)|≥(∏j=1krj)|φ(z)|kare φ(z)=czn, where c is a complex number and n is a positive integer.