Generalization of Bohr-type inequality in analytic functions

Abstract

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 $\Re f(z)<1$ 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.

24 pages

References in corpus (3)

• On the Bohr inequality
• Bohr--Rogosinski radius for analytic functions
• Modifications of Bohr's inequality in various settings

Cited by in corpus (1)

• A generalization of the Bohr-Rogosinski sum