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arXiv · 1911.05315

Refinement of the Classical Bohr Inequality

Saminathan Ponnusamy·Ramakrishnan Vijayakumar·Karl-Joachim Wirths
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Abstract

The classical inequality of Bohr asserts that if a power series converges in the unit disk and its sum has modulus less than or equal to $1$, then the sum of absolute values of its terms is less than or equal to $1$ for the subdisk $|z|<1/3$ and $1/3$ is the best possible constant. Recently, there has been a number of investigations on this topic. In this article, we present a refined version of Bohr's inequality along with few other related improved versions of previously known results.

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Saminathan Ponnusamy, Ramakrishnan Vijayakumar, Karl-Joachim Wirths. 2020-06-11. Refinement of the Classical Bohr Inequality. https://arxiv.org/abs/1911.05315

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