A note on a functional inequality
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.
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171292000553 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |