On a property of rational functions. II
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- by Q. I. Rahman PDF
- Proc. Amer. Math. Soc. 40 (1973), 143-145 Request permission
Abstract:
It is shown that if ${r_n}(z)$ is a rational function of degree $n$ such that ${r_n}(0) = 1,{\lim _{|z| \to \infty }}|{r_n}(z)| = 0$ and all its poles lie in $|{\zeta _1}| \leqq |z| \leqq 1$ then ${\max _{|z| = \rho < |{\zeta _1}|}}|{r_n}(z)| \geqq 1/(1 - {\rho ^n})$.References
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Q. I. Rahman and Paul Turán, On a property of rational functions, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. (to appear).
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 143-145
- MSC: Primary 30A04
- DOI: https://doi.org/10.1090/S0002-9939-1973-0357746-7
- MathSciNet review: 0357746