Generalization of Bohr-type inequality in analytic functions
| Autor: | Lin, Rou-Yuan, Liu, Ming-Sheng, Ponnusamy, Saminathan |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This paper mainly uses the nonnegative continuous function $\{\zeta_n(r)\}_{n=0}^{\infty}$ to redefine the Bohr radius for the class of analytic functions satisfying $\real f(z)<1$ in the unit disk $|z|<1$ and redefine the Bohr radius of the alternating series $A_f(r)$ with analytic functions $f$ of the form $f(z)=\sum_{n=0}^{\infty}a_{pn+m}z^{pn+m}$ in $|z|<1$. In the latter case, one can also get information about Bohr radius for even and odd analytic functions. Moreover, the relationships between the majorant series $M_f(r)$ and the odd and even bits of $f(z)$ are also established. We will prove that most of results are sharp. Comment: 24 pages |
| Databáze: | arXiv |
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