Bohr phenomenon for analytic functions subordinate to starlike or convex functions

Hamada, Hidetaka

doi:10.1016/j.jmaa.2021.125019

Cited by 10 publications

(6 citation statements)

References 31 publications

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“…when N = 1 and k → ∞, the lemma was obtained by Bhowmik and Das [6]. Various interesting applications of this lemma can be seen in [31,6,37,9,13].…”

Section: Introductionmentioning

confidence: 95%

A generalized Bohr-Rogosinski phenomenon

Gangania¹,

Kumar²

2022

Preprint

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“…when N = 1 and k → ∞, the lemma was obtained by Bhowmik and Das [6]. Various interesting applications of this lemma can be seen in [31,6,37,9,13].…”

Section: Introductionmentioning

confidence: 95%

A generalized Bohr-Rogosinski phenomenon

Gangania¹,

Kumar²

2022

Preprint

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“…In [34], Lie et al studied two refined versions of the Bohr inequality and determine the Bohr radius for the derivatives of analytic functions associated with quasisubordination. Bohr's phenomenon for analytic functions subordinate to starlike or convex function is investigated by Hamada in [24]. Recently, Ponnusamy et al [37] obtained the following refined versions of the Bohr-type inequalities.…”

Section: Bohr Phenomenon For the Class Of Subordinationsmentioning

confidence: 99%

“…Throughout the article, we denote the class of functions f subordinate to a function Many authors have studied Bohr phenomenon for functions in the class where the function g belongs to different class (see [1, 16, 24, 37]).…”

Section: Introductionmentioning

confidence: 99%

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

Ahammed¹,

Ahamed²

2023

Can. Math. Bull.

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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.

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“…The sharpness part in the case of subordination and quasi-subordination is dealt in [33]. The author [16] established Bohr's inequality for analytic functions subordinate to starlike or convex functions. The open problem about the theorem of Bohr for odd analytic functions raised by Ali et al [6] has been solved in a more general form by Kayumov and Ponnusamy [22].…”

Section: Introductionmentioning

confidence: 99%

Bohr's inequality for holomorphic and pluriharmonic mappings with values in complex Hilbert spaces

Hamada

2023

Mathematische Nachrichten

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Let double-struckBH$\mathbb {B}_H$ be the unit ball of a complex Hilbert space H. First, we give a Bohr's inequality for the holomorphic mappings with lacunary series with values in complex Hilbert balls. Next, we give several results on Bohr's inequality for pluriharmonic mappings with values in ℓ2. Note that the Bohr phenomenons that we have obtained are completely different from those in the case with values in C$\mathbb {C}$ and are sharp in the case with values in ℓ2.

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Bohr phenomenon for analytic functions subordinate to starlike or convex functions

Cited by 10 publications

References 31 publications

A generalized Bohr-Rogosinski phenomenon

A generalized Bohr-Rogosinski phenomenon

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

Bohr's inequality for holomorphic and pluriharmonic mappings with values in complex Hilbert spaces

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