On close-to-convex harmonic mappings

Bshouty, Daoud; Joshi, Sayali S.; Joshi, S. B.

doi:10.1080/17476933.2011.647002

Cited by 21 publications

(6 citation statements)

References 5 publications

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“…In 1984, Clunie and Sheil-Small [6] investigated the class S H and its geometric subclasses. Since then, the class S H and its subclasses have been extensively studied (see [4], [5], [6], [14], [32]). A domain Ω is called starlike with respect to a point z 0 ∈ Ω if the line segment joining z 0 to any point in Ω lies in Ω.…”

Section: Hence For Any Functionmentioning

confidence: 99%

On a subclass of harmonic close-to-convex mappings

Ghosh

Allu

2017

Monatsh Math

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Let H denote the class of harmonic functions f in D := {z ∈ C : |z| < 1} normalized by f (0) = 0 = f z (0) − 1. For α ≥ 0, we consider the following classIn this paper, we first prove the coefficient conjecture of Clunie and Sheil-Small for functions in the class W 0 H (α). We also prove growth theorem, convolution, convex combination properties for functions in the class W 0 H (α). Finally, we determine the value of r so that the partial sums of functions in the class W 0 H (α) are closeto-convex in |z| < r.1991 Mathematics Subject Classification. Primary 30C45, 30C80.

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Section: Hence For Any Functionmentioning

confidence: 99%

On a subclass of harmonic close-to-convex mappings

Ghosh

Allu

2017

Monatsh Math

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“…In [13], Chen et al obtained some results of the class M(α, −1/2) with |α| = 1. We refer to [22][23][24][25][26][27][28] for discussions on close-to-convex harmonic mappings.…”

Section: Introductionmentioning

confidence: 99%

On a subclass of close-to-convex harmonic mappings

Sun

Rasila

2016

Complex Variables and Elliptic Equations

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We introduce a new subclass M(α, β) of close-to-convex harmonic mappings in the unit disk, which originates from the work of P. Mocanu on univalent mappings. We also give coefficient estimates, and discuss the Fekete-Szegő problem, for this class of mappings. Furthermore, we consider growth, covering and area theorems of the class. In addition, we determine a disk |z| < r in which the partial sum s m,n (f )(z) is closeto-convex for each function of the class M(α, β). Finally, for certain values of the parameters α and β, we solve the radii problems related to starlikeness and convexity of functions of this class. ARTICLE HISTORY

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“…In 1984, Clunie and Sheil-Small [3] investigated the class S H together with some of its geometric subclasses. For recent results in harmonic mappings, we refer to [2,6,8,13,19,23] and the references therein. In [7], Hernández and Martin introduced the concept of stable harmonic mappings.…”

Section: Introductionmentioning

confidence: 99%

On a subclass of close-to-convex harmonic mappings

Manivannan¹,

Prajapat²

2021

Preprint

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For α > −1 and β > 0, let B 0 H (α, β) denote the class of sense preserving harmonic mappingsFirst, we establish that each function belonging to this class is closeto-convex in the open unit disk if β ∈ (0, 1 + α]. Next, we obtain coefficient bounds, growth estimates and convolution properties. We end the paper with applications and will construct harmonic univalent polynomials belonging to this class.

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On close-to-convex harmonic mappings

Cited by 21 publications

References 5 publications

On a subclass of harmonic close-to-convex mappings

On a subclass of harmonic close-to-convex mappings

On a subclass of close-to-convex harmonic mappings

On a subclass of close-to-convex harmonic mappings

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