Bohr Inequality for Odd Analytic Functions

By Ilgiz R. Kayumov, Saminathan Ponnusamy. 2017

99 citations recorded by the source corpus.

We determine the Bohr radius for the class of odd functions f satisfying $$|f(z)|\le 1$$|f(z)|≤1 for all $$|z|<1$$|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.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2eb0f98f5a29840968d0301c4e480684d13dba42

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In Applied Mathematics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Improved version of Bohr's inequality (2018, background): “Furthermore, the present authors in [9] demonstrated the following inequality for the coefficients of f : ∞ ∑ k=1 |ak|(2)r ≤ r(1 − |a0| 2)2 1 − |a0|2r .”
Bohr radius for locally univalent harmonic mappings (2017, methodology): “As in the symmetric case of analytic functions (see [2,11,12]), we have the following analog result for harmonic functions.”
Multidimensional analogues of refined Bohr’s inequality (2020, background): “In particular, after the appearance of some recent articles [9, 23, 24, 25], several new problems on Bohr’s inequality in the plane case are investigated (cf.”
Sharp Bohr type inequality (2020, methodology): “See [25, 26, 28] for new proofs of it in a general form.”
Bohr Radius for Subordination and K-quasiconformal Harmonic Mappings (2019, result): “Some of the recent results from [4, 13–15] are included in the latest two surveys.”
On a powered Bohr inequality (2018, methodology): “71] What is the exact value of the (powered) Bohr radius ρp, p ∈ (1, 2)? Is it true that ρp = rp? Using the method of proofs of our recent approach from [12,13], we solve this problem affirmatively in the following form.”
Bohr--Rogosinski radius for analytic functions (2017, background): “Furthermore, the present authors in [8] demonstrated the following inequality for the coefficients of f : (14) ∞”
On the Bohr inequality with a fixed zero coefficient (2019, background): “In [18], Kayumov and Ponnusamy also discussed Bohr’s radius for the class of analytic functions g, when g is subordinate to a member of the class of odd univalent functions.”