Generalization of Bohr-type inequality in analytic functions

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 fu...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Rou-Yuan Lin, Ming-Sheng, Liu, Saminathan Ponnusamy
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.06.2021
Subjects
Analytic functions
Continuity (mathematics)
Mathematical analysis
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422