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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| 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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| _version_ | 1850234952566702080 |
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| author | Horst Alzer |
| author_facet | Horst Alzer |
| author_sort | Horst Alzer |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-17c5213b2b364ae7b8d2e6b773c5131d |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-17c5213b2b364ae7b8d2e6b773c5131d2025-08-20T02:02:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115241341510.1155/S0161171292000553A note on a functional inequalityHorst Alzer0Department of Pure Mathematics, Applies Mathematics and Astronomy, University of South Africa, P.O. Box 392, Pretoria 0001, South AfricaWe 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.http://dx.doi.org/10.1155/S0161171292000553functional inequalityentire functions. |
| spellingShingle | Horst Alzer A note on a functional inequality International Journal of Mathematics and Mathematical Sciences functional inequality entire functions. |
| title | A note on a functional inequality |
| title_full | A note on a functional inequality |
| title_fullStr | A note on a functional inequality |
| title_full_unstemmed | A note on a functional inequality |
| title_short | A note on a functional inequality |
| title_sort | note on a functional inequality |
| topic | functional inequality entire functions. |
| url | http://dx.doi.org/10.1155/S0161171292000553 |
| work_keys_str_mv | AT horstalzer anoteonafunctionalinequality AT horstalzer noteonafunctionalinequality |