Coefficient estimates and radii problems for certain classes of polyharmonic mappings

J. Chen; A. Rasila; X. Wang

doi:10.1080/17476933.2014.936862

Coefficient estimates and radii problems for certain classes of polyharmonic mappings

J. Chen, A. Rasila^*, X. Wang

^*Corresponding author for this work

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

10 Scopus citations

Abstract

We give coefficient estimates for a class of close-to-convex harmonic mappings (Formula presented.) , and discuss the Fekete–Szegő problem of it. We also determine a disk (Formula presented.) in which the partial sum (Formula presented.) is close-to-convex for each (Formula presented.). Then, we introduce two classes of polyharmonic mappings (Formula presented.) and (Formula presented.) , consider the starlikeness and convexity of them and obtain coefficient estimates for them. Finally, we give a necessary condition for a mapping (Formula presented.) to be in the class (Formula presented.).

Original language	English
Pages (from-to)	354-371
Number of pages	18
Journal	Complex Variables and Elliptic Equations
Volume	60
Issue number	3
DOIs	https://doi.org/10.1080/17476933.2014.936862
State	Published - 4 Mar 2015
Externally published	Yes

Keywords

close-to-convex
coefficient estimates
convex
harmonic mapping
partial sum
polyharmonic mapping
starlike
the Fekete–Szegő problem

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10.1080/17476933.2014.936862

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title = "Coefficient estimates and radii problems for certain classes of polyharmonic mappings",

abstract = "We give coefficient estimates for a class of close-to-convex harmonic mappings (Formula presented.) , and discuss the Fekete–Szeg{\H o} problem of it. We also determine a disk (Formula presented.) in which the partial sum (Formula presented.) is close-to-convex for each (Formula presented.). Then, we introduce two classes of polyharmonic mappings (Formula presented.) and (Formula presented.) , consider the starlikeness and convexity of them and obtain coefficient estimates for them. Finally, we give a necessary condition for a mapping (Formula presented.) to be in the class (Formula presented.).",

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author = "J. Chen and A. Rasila and X. Wang",

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year = "2015",

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T1 - Coefficient estimates and radii problems for certain classes of polyharmonic mappings

AU - Chen, J.

AU - Rasila, A.

AU - Wang, X.

PY - 2015/3/4

Y1 - 2015/3/4

N2 - We give coefficient estimates for a class of close-to-convex harmonic mappings (Formula presented.) , and discuss the Fekete–Szegő problem of it. We also determine a disk (Formula presented.) in which the partial sum (Formula presented.) is close-to-convex for each (Formula presented.). Then, we introduce two classes of polyharmonic mappings (Formula presented.) and (Formula presented.) , consider the starlikeness and convexity of them and obtain coefficient estimates for them. Finally, we give a necessary condition for a mapping (Formula presented.) to be in the class (Formula presented.).

AB - We give coefficient estimates for a class of close-to-convex harmonic mappings (Formula presented.) , and discuss the Fekete–Szegő problem of it. We also determine a disk (Formula presented.) in which the partial sum (Formula presented.) is close-to-convex for each (Formula presented.). Then, we introduce two classes of polyharmonic mappings (Formula presented.) and (Formula presented.) , consider the starlikeness and convexity of them and obtain coefficient estimates for them. Finally, we give a necessary condition for a mapping (Formula presented.) to be in the class (Formula presented.).

KW - close-to-convex

KW - coefficient estimates

KW - convex

KW - harmonic mapping

KW - partial sum

KW - polyharmonic mapping

KW - starlike

KW - the Fekete–Szegő problem

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DO - 10.1080/17476933.2014.936862

M3 - 文章

AN - SCOPUS:84937250629

SN - 1747-6933

VL - 60

SP - 354

EP - 371

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 3

ER -

Coefficient estimates and radii problems for certain classes of polyharmonic mappings

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