Coefficients Estimate for Harmonic v-Bloch Mappings and Harmonic K-Quasiconformal Mappings

Zhu, Jianfeng

doi:10.1007/s40840-015-0175-4

Cited by 11 publications

(4 citation statements)

References 8 publications

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“…The classical Landau Theorem for bounded analytic functions states that if f is analytic in D with the normalizations f (0) = 0 and f (0 [44]). Chen et al [25] have obtained an analogue of the Landau theorem for bounded harmonic mappings in D. Several authors have considered Landau-type theorems for harmonic mappings afterwards and improved their result (see [28,43,44,49,50]). Landau's Theorem has also been extended for the classes of biharmonic mappings (see [1,26]).…”

Section: Landau's Theorem For Harmonic Bloch Mappings On the Disk ω γmentioning

confidence: 99%

On Bloch norm and Bohr phenomenon for harmonic Bloch functions on simply connected domains

Allu¹,

Halder²

2021

Preprint

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In this article, we introduce the class B * H,Ω (α) of harmonic α-Bloch-type mappings on Ω as a generalization of the class B H,Ω (α) of harmonic α-Bloch mappings on Ω, where Ω is arbitrary proper simply connected domain in the complex plane. We study several interesting properties of the classes B H,Ω (α) and B * H,Ω (α) on arbitrary proper simply connected domain Ω and on the shifted disk Ω γ containing D, whereWe establish the Landau's theorem for the harmonic Bloch space B H,Ωγ (α), we define the Bloch-Bohr radius for the space B H,Ω (α) (respectively B * H,Ω (α)) to be the largest radius r Ω,f ∈ (0, 1) such thatand for all f ∈ B H,Ω (α) (respectively B * H,Ω (α)). We investigate Bloch-Bohr radius for the classes B H,Ω (α) and B * H,Ω (α) on simply connected domain Ω containing D.

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Section: Landau's Theorem For Harmonic Bloch Mappings On the Disk ω γmentioning

confidence: 99%

On Bloch norm and Bohr phenomenon for harmonic Bloch functions on simply connected domains

Allu¹,

Halder²

2021

Preprint

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“…then f is called K-quasiconformal harmonic mapping on D, where K = 1+k 1−k ≥ 1 (cf. [11,19], and also [21] for some recent investigation on harmonic K-quasiconformal self-mapping of D). Obviously k → 1 corresponds to the case K → ∞.…”

Section: Introductionmentioning

confidence: 99%

Bohr Radius for Subordination and K-quasiconformal Harmonic Mappings

Liu

Ponnusamy

2019

Bull. Malays. Math. Sci. Soc.

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The present article concerns the Bohr radius for K-quasiconformal sense-preserving harmonic mappings f = h + g in the unit disk D for which the analytic part h is subordinated to some analytic function ϕ, and the purpose is to look into two cases: when ϕ is convex, or a general univalent function in D. The results state that if h(z) = ∞ n=0 a n z n and g(z) = ∞ n=1 b n z n , then ∞ n=1 (|a n | + |b n |)r n ≤ dist(ϕ(0), ∂ϕ(D)) for r ≤ r * and give estimates for the largest possible r * depending only on the geometric property of ϕ(D) and the parameter K. Improved versions of the theorems are given for the case when b 1 = 0 and corollaries are drawn for the case when K → ∞.2010 Mathematics Subject Classification. Primary: 30A10, 30C45, 30C62; Secondary: 30C75.

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“…Results similar to the Bloch and Landau theorems have been obtained for harmonic mappings in D under suitable conditions (see [8,14,15]). Several authors have considered Landau-type theorems for harmonic mappings afterwards and improved their result (see [11,18,20,21,25,26]). Landau's Theorem has also been extended for the classes of biharmonic mappings (see [1,9]).…”

Section: Introductionmentioning

confidence: 99%

Landau's theorem for harmonic Bloch functions on simply connected domains

Allu,

Halder

2024

Complex Variables and Elliptic Equations

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For α ∈ (0, ∞), let B H,Ω (α) denote the class of harmonic α-Bloch mappings on a proper simply connected domain Ω ⊆ C. In this article, we study coefficient estimates for harmonic α-Bloch mappings on a proper simply connected domain containing the unit disk. Furthermore, we establish the Landau's theorem and coefficient estimates for the harmonic α-Bloch space B H,Ωγ (α) on the shifted disk Ω γ , where

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Coefficients Estimate for Harmonic v-Bloch Mappings and Harmonic K-Quasiconformal Mappings

Cited by 11 publications

References 8 publications

On Bloch norm and Bohr phenomenon for harmonic Bloch functions on simply connected domains

On Bloch norm and Bohr phenomenon for harmonic Bloch functions on simply connected domains

Bohr Radius for Subordination and K-quasiconformal Harmonic Mappings

Landau's theorem for harmonic Bloch functions on simply connected domains

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