Ahlfors type p-valent conditions for biharmonic functions

被引：1

作者：

Wang, Xiaoyuan ^{[1
]}

Ponnusamy, Saminathan ^{[2
,3
]}

Fan, Jinhua ^{[1
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Math & Stat, Nanjing 210094, Jiangsu, Peoples R China

[2] Indian Inst Technol Madras, Dept Math, Chennai 600 036, Tamil Nadu, India

[3] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 537卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Harmonic and biharmonic mapping; Ahlfors's univalence condition; Multivalent function; Quasiconformal extension; HARMONIC-MAPPINGS; UNIVALENCE CONDITIONS; PRE-SCHWARZIAN; EXTENSION; CRITERIA;

D O I：

10.1016/j.jmaa.2024.128273

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1973, Ahlfors established a sufficient condition for an analytic function to be univalent in the unit disk |z| < 1 and has a quasiconformal extension. Using his result, many known conditions for univalence and quasiconformal extendibility of analytic functions in the unit disk were deduced. Interestingly, his result was generalized to the class of harmonic mappings. The main aim of this paperlis to present apother generalization of Ahlfors's result by establishing p-valent conditions for biharmonic mappings defined in the unit disk and exterior. Moreover, we also determing conditions for a harmonic mapping of the unit disk to be univalent and has a quasiconformal extension.

引用

页数：20

共 36 条

[1] ONE PARAMETER FAMILY OF UNIVALENT BIHARMONIC MAPPINGS [J].

Abu Muhanna, Y. ;

Bharanedhar, S. V. ;

Ponnusamy, S. .

TAIWANESE JOURNAL OF MATHEMATICS, 2014, 18 (04) :1151-1169

[2]

Ahlfors Lars V., 1974, ANN MATH STUD, V79, P23

[3]

Avhadiev F.G., 1975, Mat. Zametki, V18, P793

[4] Becker type univalence conditions for harmonic mappings [J].

Avkhadiev F.G. ;

Nasibullin R.G. ;

Shafigullin I.K. .

Russian Mathematics, 2016, 60 (11) :69-73

[5]

Avkhadiev F.G, 1996, Monografii pomatematike

[6]

Avkhadiev F.G., 1992, Tr. Semin. Kraev. Zadacham, P3

[7]

BECKER J, 1984, J REINE ANGEW MATH, V354, P74

[8]

BECKER J, 1972, J REINE ANGEW MATH, V255, P23

[9]

Bshouty D, 2005, HANDBOOK OF COMPLEX ANALYSIS: GEOMETRIC FUNCTION THEORY, VOL 2, P479

[10] Properties of Some Classes of Planar Harmonic and Planar Biharmonic Mappings [J].

Chen, S. H. ;

Ponnusamy, S. ;

Wang, X. .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2011, 5 (03) :901-916

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