INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES
Let \(\Re_n\) be the set of all rational functions of the type \(r(z) = p(z)/w(z),\) where \(p(z)\) is a polynomial of degree at most \(n\) and \(w(z) = \prod_{j=1}^{n}(z-a_j)\), \(|a_j|>1\) for \(1\leq j\leq n\). In this paper, we set up some results for rational functions with fixed poles and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2022-12-01
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| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/455 |
| Summary: | Let \(\Re_n\) be the set of all rational functions of the type \(r(z) = p(z)/w(z),\) where \(p(z)\) is a polynomial of degree at most \(n\) and \(w(z) = \prod_{j=1}^{n}(z-a_j)\), \(|a_j|>1\) for \(1\leq j\leq n\). In this paper, we set up some results for rational functions with fixed poles and restricted zeros. The obtained results bring forth generalizations and refinements of some known inequalities for rational functions and in turn produce generalizations and refinements of some polynomial inequalities as well. |
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| ISSN: | 2414-3952 |