Bohr inequality for odd analytic functions

2017/01/14 by Kayumov, Ilgiz R, Ponnusamy, Saminathan · 8 citations
#30C35 #30H05 #Complex Variables (math.CV) #FOS: Mathematics #Primary 30A10 #Secondary 30C45

paper · doi:10.48550/arxiv.1701.03884

Abstract

We determine the Bohr radius for the class of odd functions f satisfying |f(z)|≤ 1 for all |z|<1, settling the recent conjecture of Ali, Barnard and Solynin \citeAliBarSoly. 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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• Improved Bohr inequalities involving Fréchet derivatives associated with Holomorphic mappings in Banach spaces
• Multidimensional analogues of the refined Bohr type inequalities
• Multidimensional analogues of the improved Bohr's inequality
• Bohr inequalities for holomorphic mappings in higher-dimensional complex Banach spaces
• Estimates of the Second Bohr radius for vector-valued Holomorphic functions
• Bohr Phenomenon for K-quasiconformal Harmonic Mappings Involving One Parameter
• The Bohr inequality for vector-valued holomorphic functions with lacunary series in complex Banach spaces
• Bohr inequality and Bohr-Rogosinski inequality for K-Quasiconformal harmonic mappings

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