The Bohr phenomenon for analytic functions on shifted disks

Ahamed, Molla Basir; Allu, Vasudevarao; Halder, Himadri

doi:10.54330/afm.112561

Cited by 17 publications

(9 citation statements)

References 22 publications

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“…Let be the class of analytic functions , and let denote the class of functions such that . For the class , the Bohr radius is defined by (see [4, 16]) where is the Bohr operator for in . For , reduces to , which is the classical Bohr radius for the class .…”

Section: Introductionmentioning

confidence: 99%

“…In 2010, Fournier and Ruscheweyh [16] extensively studied the Bohr radius problem for arbitrary simply connected domains containing D. Let H(Ω) be the class of analytic functions f ∶ Ω → C, and let B(Ω) denote the class of functions f ∈ H(Ω) such that f (Ω) ⊆ D. For the class B(Ω), the Bohr radius B Ω is defined by (see [4,16])…”

Section: Introductionmentioning

confidence: 99%

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Bohr operator on operator-valued polyanalytic functions on simply connected domains

Allu

Halder²

2023

Can. Math. Bull.

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In this article, we study the Bohr operator for the operator-valued subordination class $S(f)$ consisting of holomorphic functions subordinate to f in the unit disk $\mathbb {D}:=\{z \in \mathbb {C}: |z|<1\}$ , where $f:\mathbb {D} \rightarrow \mathcal {B}(\mathcal {H})$ is holomorphic and $\mathcal {B}(\mathcal {H})$ is the algebra of bounded linear operators on a complex Hilbert space $\mathcal {H}$ . We establish several subordination results, which can be viewed as the analogs of a couple of interesting subordination results from scalar-valued settings. We also obtain a von Neumann-type inequality for the class of analytic self-mappings of the unit disk $\mathbb {D}$ which fix the origin. Furthermore, we extensively study Bohr inequalities for operator-valued polyanalytic functions in certain proper simply connected domains in $\mathbb {C}$ . We obtain Bohr radius for the operator-valued polyanalytic functions of the form $F(z)= \sum _{l=0}^{p-1} \overline {z}^l \, f_{l}(z) $ , where $f_{0}$ is subordinate to an operator-valued convex biholomorphic function, and operator-valued starlike biholomorphic function in the unit disk $\mathbb {D}$ .

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bohr operator on operator-valued polyanalytic functions on simply connected domains

Allu

Halder²

2023

Can. Math. Bull.

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“…The quantity S r plays a significant role in the study of improved versions of the classical Bohr inequality and with the help of this quantity, in the recent years, many Bohr-type inequalities are obtained (see e.g. [8,37,38,50]). For example, in 2020, Kayumov and Ponnusamy [43] established the following improved version of Bohr inequality for analytic functions.…”

Section: Introductionmentioning

confidence: 99%

Bohr phenomenon for certain classes of harmonic mappings

Ahamed¹,

Allu²

2022

Rocky Mountain J. Math.

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The Bohr radius for the class of harmonic functions of the form f (zholds for |z| = r ≤ r f , where d(f (0), ∂f (D)) is the Euclidean distance between f (0) and the boundary of f (D). In this paper, we prove two-type of improved versions of the Bohr inequalities, one for certain class of harmonic and univalent functions and the other is for stable harmonic mappings. It is observed in the paper that to obtain sharp Bohr inequalities it is enough to consider any non-negative real coefficients of the quantity S r /π. As a consequence of the main result, we prove a corollaries showing the precise value of the sharp Bohr radius. ∞ n=0 a n z n converges

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“…There are lots of works about the classical Bohr inequality and its generalized forms in the recent years. For example, the notion of the Bohr radius was generalized by Abu-Muhanna and Ali [1,2] to include mappings from D to simply connected domain and to exterior of a unit disk in C. Moreover, the Bohr phenomenon for shifted disks and simply connected domains are discussed in [7,23,24,34]. Allu and Halder [9], and Bhowmik and Das [17] have considered the Bohr phenomenon for the class of subordinations.…”

Section: Introductionmentioning

confidence: 99%