Bohr-type inequalities for unimodular bounded analytic functions

Kaixin Chen; Ming-Sheng Liu; Saminathan Ponnusamy

Bohr-type inequalities for unimodular bounded analytic functions

Complex Variables 2023-02-16 v1

Authors: Kaixin Chen , Ming-Sheng Liu , Saminathan Ponnusamy

Abstract

In this paper, we establish several new versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing $\varphi=\{\varphi_n(r)\}^{\infty}_{n=0}$ in place of the $\{r^n\}^{\infty}_{n=0}$ in the power series representations of the functions involved with the Bohr sum and thereby introducing a single parameter, which generalize several related results of earlier authors.

Keywords

bohr phenomenon univalent functions inequalities

Cite

@article{arxiv.2302.07745,
  title  = {Bohr-type inequalities for unimodular bounded analytic functions},
  author = {Kaixin Chen and Ming-Sheng Liu and Saminathan Ponnusamy},
  journal= {arXiv preprint arXiv:2302.07745},
  year   = {2023}
}

Comments

13 pages. The article is with a journal

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