Inequalities Concerning Rational Functions With Prescribed Poles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908802316500992 |
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| author | Rather, N. A. Bhat, Tanveer Bhat, Danish Rashid |
| author_facet | Rather, N. A. Bhat, Tanveer Bhat, Danish Rashid |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01014 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inequalities Concerning Rational Functions With Prescribed Poles Rather, N. A. Bhat, Tanveer Bhat, Danish Rashid Complex Variables 30A10, 30C10, 30C15 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. |
| title | Inequalities Concerning Rational Functions With Prescribed Poles |
| topic | Complex Variables 30A10, 30C10, 30C15 |
| url | https://arxiv.org/abs/2602.01014 |