On polyharmonic univalent mappings

J. Chen; A. Rasila; X. Wang

On polyharmonic univalent mappings

J. Chen, A. Rasila, X. Wang

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

7 Scopus citations

Abstract

In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by HS_p(λ), and its subclass HS ^o_p(λ), where λ ∈ [0,1] is a constant. These classes are natural generalizations of a class of mappings studied by Goodman in the 1950s. We generalize the main results of Avci and Zlotkiewicz from the 1990s to the classes HS_p(λ) and HS^o _p(λ), showing that the mappings in HS_p(λ) are univalent and sense preserving. We also prove that the mappings in HS ^o_p(λ) are starlike with respect to the origin, and characterize the extremal points of the above classes.

Original language	English
Pages (from-to)	343-357
Number of pages	15
Journal	Mathematical Reports
Volume	15
Issue number	4
State	Published - 2013
Externally published	Yes

Keywords

Convexity
Extremal point
Polyharmonic mapping
Starlikeness

Cite this

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abstract = "In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by HSp(λ), and its subclass HS op(λ), where λ ∈ [0,1] is a constant. These classes are natural generalizations of a class of mappings studied by Goodman in the 1950s. We generalize the main results of Avci and Zlotkiewicz from the 1990s to the classes HSp(λ) and HSo p(λ), showing that the mappings in HSp(λ) are univalent and sense preserving. We also prove that the mappings in HS op(λ) are starlike with respect to the origin, and characterize the extremal points of the above classes.",

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T1 - On polyharmonic univalent mappings

AU - Chen, J.

AU - Rasila, A.

AU - Wang, X.

PY - 2013

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N2 - In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by HSp(λ), and its subclass HS op(λ), where λ ∈ [0,1] is a constant. These classes are natural generalizations of a class of mappings studied by Goodman in the 1950s. We generalize the main results of Avci and Zlotkiewicz from the 1990s to the classes HSp(λ) and HSo p(λ), showing that the mappings in HSp(λ) are univalent and sense preserving. We also prove that the mappings in HS op(λ) are starlike with respect to the origin, and characterize the extremal points of the above classes.

AB - In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by HSp(λ), and its subclass HS op(λ), where λ ∈ [0,1] is a constant. These classes are natural generalizations of a class of mappings studied by Goodman in the 1950s. We generalize the main results of Avci and Zlotkiewicz from the 1990s to the classes HSp(λ) and HSo p(λ), showing that the mappings in HSp(λ) are univalent and sense preserving. We also prove that the mappings in HS op(λ) are starlike with respect to the origin, and characterize the extremal points of the above classes.

KW - Convexity

KW - Extremal point

KW - Polyharmonic mapping

KW - Starlikeness

UR - http://www.scopus.com/inward/record.url?scp=84898438741&partnerID=8YFLogxK

M3 - 文章

AN - SCOPUS:84898438741

SN - 1582-3067

VL - 15

SP - 343

EP - 357

JO - Mathematical Reports

JF - Mathematical Reports

IS - 4

ER -

On polyharmonic univalent mappings

Abstract

Keywords

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