Bohr inequality for odd analytic functions

Abstract

We determine the Bohr radius for the class of odd functions $f$ satisfying $|f(z)|\le 1$ for all $|z|<1$, settling the recent conjecture of Ali, Barnard and Solynin \cite{AliBarSoly}. In fact, we solve this problem in a more general setting. Then we discuss Bohr's radius for the class of analytic functions $g$, when $g$ is subordinate to a member of the class of odd univalent functions.

8 pages

Cited by in corpus (2)

• Bohr--Rogosinski radius for analytic functions
• Bohr's inequality for analytic functions ${\sum }_k{b}_k{z}^{kp+m}$ and harmonic functions