Bohr Inequality for Odd Analytic Functions

We determine the Bohr radius for the class of odd functions f satisfying | f ( z ) | ≤ 1 for all | z | < 1 , solving the recent problem of Ali et al. (J Math Anal Appl 449(1):154–167, 2017 ). In fact, we solve this problem in a more general setting. Then we discuss Bohr’s radius for the class of...

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Published inComputational methods and function theory Vol. 17; no. 4; pp. 679 - 688
Main Authors Kayumov, Ilgiz R, Ponnusamy, Saminathan
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017
Springer Nature B.V
Subjects
Analysis
Analytic functions
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Bohr’s inequality
Schwarz lemma
symmetric functions
Primary 30A10
Analytic functions
30H05
Subordination and odd univalent functions
Secondary 30C45
30C35
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ISSN1617-9447
2195-3724
DOI10.1007/s40315-017-0206-2

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Summary:We determine the Bohr radius for the class of odd functions f satisfying | f ( z ) | ≤ 1 for all | z | < 1 , solving the recent problem of Ali et al. (J Math Anal Appl 449(1):154–167, 2017 ). 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.
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ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-017-0206-2