On the Refined Esitmates of All Homogeneous Expansions for a Subclass of Biholomorphic Starlike Mappings in Several Complex Variables

2021 ◽  
Vol 42 (6) ◽  
pp. 909-920
Author(s):  
Xiaosong Liu ◽  
Taishun Liu
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Starlike Mappings

Parabolic starlike mappings in several complex variables

2007 ◽  
Vol 123 (3) ◽  
pp. 301-324 ◽  
Author(s):  
Hidetaka Hamada ◽  
Tatsuhiro Honda ◽  
Gabriela Kohr
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Starlike Mappings

scholarly journals Research on Geometric Mappings in Complex Systems Analysis

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Yanyan Cui ◽  
Chaojun Wang ◽  
Sifeng Zhu
Keyword(s):  
Banach Spaces ◽  
Systems Analysis ◽  
Starlike Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Coefficient Estimates ◽  
Positive Real ◽  
Reinhardt Domains ◽  
Complex Order ◽  
Starlike Mappings

We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order λ, in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order λ. By the properties of functions with positive real parts and considering the zero of order k, we obtain the coefficient estimates for almost starlike functions of complex order λ on D. We also discuss the invariance of almost starlike mappings of complex order λ on Reinhardt domains and on the unit ball B in complex Banach spaces. The conclusions contain and generalize some known results.

scholarly journals On the Fekete and Szegö Problem for the Class of Starlike Mappings in Several Complex Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qing-Hua Xu ◽  
Tai-Shun Liu
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Unit Disk ◽  
Univalent Functions ◽  
Complex Banach Space ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Unit Polydisk ◽  
Starlike Mappings

LetSbe the familiar class of normalized univalent functions in the unit disk. Fekete and Szegö proved the well-known resultmaxf∈S⁡a3-λa22=1+2e-2λ/(1-λ)forλ∈0, 1. We investigate the corresponding problem for the class of starlike mappings defined on the unit ball in a complex Banach space or on the unit polydisk inCn, which satisfies a certain condition.

scholarly journals A Note on Strongly Starlike Mappings in Several Complex Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Hidetaka Hamada ◽  
Tatsuhiro Honda ◽  
Gabriela Kohr ◽  
Kwang Ho Shon
Keyword(s):  
Unit Ball ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Biholomorphic Mapping ◽  
Strongly Starlike ◽  
Starlike Mappings ◽  
Euclidean Unit Ball

Letfbe a normalized biholomorphic mapping on the Euclidean unit ball𝔹ninℂnand letα∈0,1. In this paper, we will show that iffis strongly starlike of orderαin the sense of Liczberski and Starkov, then it is also strongly starlike of orderαin the sense of Kohr and Liczberski. We also give an example which shows that the converse of the above result does not hold in dimensionn≥2.

Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables

2019 ◽  
Vol 69 (4) ◽  
pp. 843-856
Author(s):  
Zhenhan Tu ◽  
Liangpeng Xiong
Keyword(s):  
Banach Space ◽  
Convex Function ◽  
Starlike Functions ◽  
Complex Banach Space ◽  
Circular Domain ◽  
Complex Variables ◽  
Several Complex Variables ◽  
The Family ◽  
Unit Polydisk ◽  
Starlike Mappings

Abstract Let $\begin{array}{} \mathcal {S}^*_\psi \end{array}$ be a subclass of starlike functions in the unit disk 𝕌, where ψ is a convex function such that ψ(0) = 1, ψ′(0) > 0, ℜ(ψ(ξ)) > 0 and ψ(𝕌) is symmetric with respect to the real axis. We obtain the sharp solution of Fekete-Szegö problem for the family $\begin{array}{} \mathcal {S}^*_\psi \end{array}$, and then extend the result to the case of corresponding subclass defined on the bounded starlike circular domain Ω in several complex variables, which give an unified answer of Fekete-Szegö problem for the kinds of subclasses of starlike mappings defined on Ω. At last, we propose two conjectures related the same problems on the unit ball in a complex Banach space and on the unit polydisk in ℂn.

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