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Refined Bohr inequalities for certain classes of functions: analytic, univalent, and convex

Part of: General properties Geometric function theory Spaces and algebras of analytic functions

Published online by Cambridge University Press:  09 June 2023

Sabir Ahammed Open the ORCID record for Sabir Ahammed [Opens in a new window]  and
Molla Basir Ahamed Open the ORCID record for Molla Basir Ahamed [Opens in a new window]
Sabir Ahammed
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India e-mail: sabira.math.rs@jadavpuruniversity.in
Molla Basir Ahamed*
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India e-mail: sabira.math.rs@jadavpuruniversity.in
*
e-mail: mbahamed.math@jadavpuruniversity.in
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Abstract

In this article, we prove several refined versions of the classical Bohr inequality for the class of analytic self-mappings on the unit disk $ \mathbb {D} $, class of analytic functions $ f $ defined on $ \mathbb {D} $ such that $\mathrm {Re}\left (f(z)\right )<1 $, and class of subordination to a function g in $ \mathbb {D} $. Consequently, the main results of this article are established as certainly improved versions of several existing results. All the results are proved to be sharp.

Keywords

Bounded analytic functionsBohr inequalityBohr–Rogosinski inequalitySchwarz–Pick lemma

MSC classification

Primary: 30A10: Inequalities in the complex domain 30H05: Bounded analytic functions 30C35: General theory of conformal mappings
Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 1 , March 2024 , pp. 9 - 25
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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