The Bohr phenomenon for analytic functions on shifted disks

Authors

  • Molla Basir Ahamed Indian Institute of Technology Bhubaneswar, School of Basic Science
  • Vasudevarao Allu Indian Institute of Technology Bhubaneswar, School of Basic Science
  • Himadri Halder Indian Institute of Technology Bhubaneswar, School of Basic Science
DOI: https://doi.org/10.54330/afm.112561

Keywords:

Simply connected domain, bounded analytic functions, improved Bohr radius, Bohr-Rogosinski radius, refined Bohr radius and Bohr inequality

Abstract

In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain \(\Omega_{\gamma}=\bigg\{z\in\mathbb{C} \colon \bigg|z+\frac{\gamma}{1-\gamma}\bigg|<\frac{1}{1-\gamma}\bigg\}\) for \(0\leq \gamma<1.\) We study improved Bohr radius, Bohr-Rogosinski radius and refined Bohr radius for the class of analytic functions defined in \(\Omega_{\gamma}\), and obtain several sharp results.
Issue
Vol. 47 No. 1 (2022)
Section
Articles

Published

2021-12-02

How to Cite

Ahamed, M. B., Allu, V., & Halder, H. (2021). The Bohr phenomenon for analytic functions on shifted disks. Annales Fennici Mathematici, 47(1), 103–120. https://doi.org/10.54330/afm.112561

Copyright (c) 2021 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.