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.

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.

scholarly journals Geometric Mappings under the Perturbed Extension Operators in Complex Systems Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Chaojun Wang ◽  
Yanyan Cui ◽  
Hao Liu
Keyword(s):  
Complex Systems ◽  
Unit Ball ◽  
Systems Analysis ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Geometric Properties ◽  
Geometric Characteristics ◽  
New Approaches ◽  
Special Cases ◽  
Hartogs Domains

In this paper, we mainly seek conditions on which the geometric properties of subclasses of biholomorphic mappings remain unchanged under the perturbed Roper-Suffridge extension operators. Firstly we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Secondly, applying the analytical characteristics and growth results of subclasses of biholomorphic mappings, we conclude that the generalized Roper-Suffridge operators preserve the geometric properties of strong and almost spiral-like mappings of typeβand orderα,SΩ⁎(β,A,B)as well as almost spiral-like mappings of typeβand orderαunder different conditions on Bergman-Hartogs domains. Sequentially we obtain the conclusions on the unit ballBnand for some special cases. The conclusions include and promote some known results and provide new approaches to construct biholomorphic mappings which have special geometric characteristics in several complex variables.

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

First Steps in Several Complex Variables: Reinhardt Domains

10.4171/049 ◽  
2008 ◽  
Author(s):  
Marek Jarnicki ◽  
Peter Pflug
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Reinhardt Domains

Sharp growth theorems and coefficient bounds for starlike mappings in several complex variables

2008 ◽  
Vol 29 (4) ◽  
pp. 353-368 ◽  
Author(s):  
Hidetaka Hamada ◽  
Tatsuhiro Honda
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Coefficient Bounds ◽  
Sharp Growth ◽  
Starlike Mappings

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.

Sharp coefficient estimates for certain subclasses of starlike functions of complex order

2013 ◽  
Vol 225 ◽  
pp. 43-49 ◽  
Author(s):  
Qing-Hua Xu ◽  
Qiao-Min Cai ◽  
H.M. Srivastava
Keyword(s):  
Starlike Functions ◽  
Coefficient Estimates ◽  
Complex Order

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.

scholarly journals ON SHARP INEQUALITIES OF HOMOGENEOUS EXPANSIONS FOR STARLIKE MAPPINGS OF ORDER $\alpha$ IN SEVERAL COMPLEX VARIABLES

2013 ◽  
Vol 17 (3) ◽  
pp. 801-813 ◽  
Author(s):  
Xiaosong Liu ◽  
Taishun Liu ◽  
Qinghua Xu
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Starlike Mappings
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