On a subclass of close-to-convex harmonic mappings

Yong Sun; Yue Ping Jiang; Antti Rasila

doi:10.1080/17476933.2016.1193493

On a subclass of close-to-convex harmonic mappings

Yong Sun, Yue Ping Jiang, Antti Rasila^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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| in which the partial sum s_m,n(f)(z) is close-to-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.

Original language	English
Pages (from-to)	1627-1643
Number of pages	17
Journal	Complex Variables and Elliptic Equations
Volume	61
Issue number	12
DOIs	https://doi.org/10.1080/17476933.2016.1193493
State	Published - 1 Dec 2016
Externally published	Yes

Keywords

Fekete–Szegő problem
Harmonic mapping
area theorem
close-to-convex function
coefficient estimate
convex function
covering theorem
growth theorem
partial sum
starlike function

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10.1080/17476933.2016.1193493

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title = "On a subclass of close-to-convex harmonic mappings",

abstract = "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-Szeg{\H o} problem, for this class of mappings. Furthermore, we consider growth, covering and area theorems of the class. In addition, we determine a disk |z| in which the partial sum sm,n(f)(z) is close-to-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.",

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AU - Jiang, Yue Ping

AU - Rasila, Antti

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N2 - 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| in which the partial sum sm,n(f)(z) is close-to-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.

AB - 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| in which the partial sum sm,n(f)(z) is close-to-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.

KW - Fekete–Szegő problem

KW - Harmonic mapping

KW - area theorem

KW - close-to-convex function

KW - coefficient estimate

KW - convex function

KW - covering theorem

KW - growth theorem

KW - partial sum

KW - starlike function

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DO - 10.1080/17476933.2016.1193493

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JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

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ER -

On a subclass of close-to-convex harmonic mappings

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