Bohr inequality for odd analytic functions

Ilgiz R Kayumov, Saminathan Ponnusamy

Published 2017-01-14Version 1

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.