1 edition of **Convex and Starlike Mappings in Several Complex Variables** found in the catalog.

- 198 Want to read
- 33 Currently reading

Published
**1998** by Springer Netherlands in Dordrecht .

Written in English

- Differential equations, partial,
- Discrete groups,
- Algebra,
- Global differential geometry,
- Mathematics,
- Functions of complex variables

This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. This is the first book which systematically studies this topic. It gathers together, and presents in a unified manner, the current state of affairs for convex and starlike biholomorphic mappings in several complex variables. The majority of the results presented are due to the author, his co-workers and his students. Audience: This volume will be of interest to research mathematicians whose work involves several complex variables and one complex variable.

**Edition Notes**

Statement | by Sheng Gong |

Series | Mathematics and Its Applications -- 435, Mathematics and Its Applications -- 435 |

Classifications | |
---|---|

LC Classifications | QA331.7 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (xiii, 209 p.) |

Number of Pages | 209 |

ID Numbers | |

Open Library | OL27027371M |

ISBN 10 | 9401061912, 9401152063 |

ISBN 10 | 9789401061919, 9789401152068 |

OCLC/WorldCa | 851367724 |

Several Complex Variables By B. Malgrange Tata Institute of Fundamental Research Bombay No part of this book may be reproduced in any form by print, microﬁlm or any other means with- equations to the case of functions of several variables).

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This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions.

This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions.

This is the first book which systematically studies this topic. Several Complex Variables and Analytic Spaces *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis.

ebook access is temporary and does not include ownership of the ebook. Convex and Starlike Mappings in Several Complex Variables. Authors (view affiliations) Sheng Gong; k Downloads; Part of the Mathematics and Its Applications book series (MAIA, volume ) Log in to check access.

Buy eBook. USD Buy eBook. USD The distortion theorem for holomorphic convex and starlike mappings. Sheng Gong. Find many great new & used options and get the best deals for Mathematics and Its Applications: Convex and Starlike Mappings in Several Complex Variables by Sheng Gong and Sheng Kung (, Hardcover) at the best online prices at eBay.

Free shipping for many products. This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. This is the first book which systematically studies.

Gong S. () The distortion theorem for holomorphic convex and starlike mappings. In: Convex and Starlike Mappings in Several Complex Variables. Mathematics and Its Applications, vol Author: Sheng Gong.

It is proved that the class of ε quasi-convex mappings is a proper subset of the class of starlike mappings and contains the class of ε starlike mappings properly for some ε∈[−1,0)∪(0,1].

and are complex constants.Formula (2) can be regarded as a generalization of the Christoffel–Schwarz formula for mappings of the disc onto convex polygons. Let be the class of all convex functions in normalized by the conditions, ; let, be the subclasses of consisting of functions that map onto convex domains of the -plane with a -fold symmetry of rotation about the point.

CONVEX MAPPINGS IN SEVERAL COMPLEX VARIABLES HIDETAKA HAMADA AND GABRIELA KOHR Kyushy Kyoritsu Univ., Japan and Babe§-Bolyai Univ., Romania ABSTRACT.

Let B be the unit ball of en with respect to an arbitrary norm. We will give a sufficient condition for a local diffeomorphism of C1 class on B to be univalent and to have a convex image. Finally. Let B n be the Euclidean unit ball in C n.

In this paper, we study several properties of strongly starlike mappings of order α (0. It introduces the infinite-dimensional theory and provides numerous exercises in each chapter for further study.

The authors present such topics as linear invariance in the unit disc, Bloch functions and the Bloch constant, and growth, covering and distortion results for starlike and. G-LOEWNER CHAINS AND PARABOLIC STARLIKE MAPPINGS IN SEVERAL COMPLEX VARIABLES1 S.

Rahrovi, A. Ebadian and S. Shams Abstract Let f be a locally univalent function on the unit disc and Q: Cn → Cbea homogenous polynomial of degree 2. We consider the normalized extension of f to the Euclidean unit ball Bn ⊆ C given by [Φn,Q(f)](z) = (f(z1)+f.

Distortion Theorems for Almost Convex Mappings of Order in Several Complex Variables 1XIAOSONG LIU, 2TAISHUN IU AND 3QINGHUA XU 1School of Mathematics and Computation Science, Zhanjiang Normal University, Zhanjiang, Guangdong2Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang3College of Mathematics and Information.

In the Sections 3 and 4 we introduce and study the classes of starlike, con-vex and alpha-convex functions of hyperbolic complex and of dual complex variable, respectively. The methods were suggested by the classical ones in [].

Preliminaries First let us recall some known facts about the complex-type numbers (see e.g. [6], []). A twice continuously differentiable function of several variables is convex on a convex set if and only if its Hessian matrix of second partial derivatives is positive semidefinite on the interior of the convex set.

Any local minimum of a convex function is also a global minimum. A strictly convex function will have at most one global minimum. CONVEX AND STARLIKE UNIVALENT FUNCTIONS BY S. BERNARDI 1. Introduction.

Let (S) denote the class of functions/(z) = z + 2. anzn which are regular and univalent in \z\. Fekete and Szegö problem for a subclass of quasi-convex mappings in several complex variables.

Qinghua XU 1, * (),Ting YANG 1,Taishun LIU 2,Huiming XU 3: 1. College of Mathematics and Information Science, Jiangxi Normal University, NanchangChina 2.

In this paper, we investigate rigidity and its applications to extreme points of biholomorphic convex mappings on Reinhardt domains. By introducing a version of the scaling method, we precisely construct many unbounded convex mappings with only one infinite discontinuity on the boundary of this domain.

We also give a rigidity of these unbounded convex mappings via the Kobayashi metric and the Author: Taishun Liu, Xiaomin Tang, Jianfei Wang. A convex function. Image: Eli Osherovich. Convex or concave. It's a question we usually answer just by looking at something.

It's convex if it bulges outwards and concave if it bulges when it comes to mathematical functions, things aren't that simple. A team of computer scientists from the Massachusetts Institute of Technology have recently shown that deciding.

The main purpose of this paper is to introduce two classes P β (λ,b) and R β (λ,b) (b, a complex number with Re(b)>0) of functions which are analytic in the unit cient estimates for functions in these classes and radii of close-to convexity, starlikeness and convexity are by: The main theme is the extension of geometric function theory methods and theorems to several complex variables.

The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.

Thanks for contributing an answer to Mathematics Stack Exchange. Please be sure to answer the question. Provide details and share your research. But avoid Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. Geometric Function Theory in One and Higher Dimensions discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to t and growth, covering and distortion results for starlike and convex mappings in Cn and complex Banach spaces.

Instructors. Book Description. This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions.

Discover Book Depository's huge selection of Sheng Gong books online. Free delivery worldwide on over 20 million titles. Convex and Starlike Mappings in Several Complex Variables.

Sheng Gong. 30 Apr Hardback. US$ Convex and Starlike Mappings in Several Complex Variables. Sheng Gong. 06 Nov Paperback. US$ Add to. Abstract. The aim of this paper is to establish the coefficient estimates for the subclasses of -starlike and -convex functions with respect to symmetric points involving -difference certain applications based on these results for subclasses of univalent functions defined by convolution are by: 2.

several complex variables was formulated rst time by H. Cartan in the Appendix in the book of P. Montel published in [22]. The extension of the geometric properties of biholomorphic mappings was started in.

CHIN. ANN. OF MATH. Vol Ser.B mappings and some other important classes of mappings in several complex variables.

Along this direction, inthe ﬁrst aﬃrmative result about the growth and 1 4-covering theorem in several complex variables was obtained by R.

Barnard, C. Fitzgerald, S. Gong[3]. They gave the growth and 1 4-covering theorem for the class of normalized. mappings in Banach and Hilbert spaces. Following some early developments dating back to aboutthere has been a surge of recent activity in in nite-dimensional holomorphy.

Of particular interest to us are problems which combine geometrical methods of one and several complex variables with operator theory and functional analysis. Let Bnr={z ϵ Cn:¦z¦Author: Roger W. Barnard, Richard S. Varga, Kent Pearce.

Contents v 6 free Preface vii 8 free Contributors xi 12 free Complex Geometry in China 1 14 free Biholomorphic Mappings in Several Complex Variables 15 28 Introduction 16 29 I. The conditions of starlikeness, convexity and univalency for a holomorphic mapping 18 31 1.

您的位置： 首页 > 科学自然 > 数学 > Entire Functions of Several Complex Variables 目录导航. 外包 游泳及跳水 变戏法 Convex and Starlike Mappings in Several Complex Variables. ISSN ISSN (Online) CN /O1 Postal Subscription Code Impact Factor: In mathematics, more precisely in complex analysis, the holomorphically convex hull of a given compact set in the n-dimensional complex space is defined as follows.

Let ⊂ be a domain (an open and connected set), or alternatively for a more general definition, let be an dimensional complex analytic r let stand for the set of holomorphic functions on. This volume contains the proceedings of the workshop on Analysis and Geometry in Several Complex Variables, held from January 4–8,at Texas A&M University at Qatar, Doha, Qatar.

This volume covers many topics of current interest in several complex variables, CR geometry, and the related area of overdetermined systems of complex vector.

Author by: Derek K. Thomas Languange: en Publisher by: Walter de Gruyter GmbH & Co KG Format Available: PDF, ePub, Mobi Total Read: 49 Total Download: File Size: 48,9 Mb Description: The study of univalent functions dates back to the early years of the 20th century, and is one of the most popular research areas in complex book is directed at introducing and bringing.

The usual convex set is the real linear convex set, if we change the real linear map into complex linear map, we can get the complex convex set. A system way to do this is in the several complex analysis, at wiki here: Holomorphically convex hull, changing the holomorphic functions into complex linear functions.

Ponnusamy and V. Singh, Criteria for strongly starlike functions, Complex Variables: Theory and Appl. 34 (), – S. Ponnusamy and M. Vuorinen, Asymptotic expansions and inequalities for hypergeometric functions, Mathematika 44 (), – in convex analysis to correspond to the subdi erentials of the closed proper convex functions on the real line.

Here that connection is developed in terms of what those convex functions and their conjugates say about the random variables, and how that information serves in applications to stochastic Size: KB. On the Fekete and Szegö Problem for the Class of Starlike Mappings in Several Complex Variables Xu, Qing-Hua and Liu, Tai-Shun, Abstract and Applied Analysis, ; A general approach to the Fekete-Szegö problem CHOI, Jae Ho, KIM, Yong Chan, and SUGAWA, Toshiyuki, Journal of the Mathematical Society of Japan, Cited by: is a starlike convex function, since it satisﬁes both condition (1) and (2).

The same remark is also true for starlike quasi-convex functions. The function f 1 is a restriction to X of the convex function f 2: R2 → R, where f 2(x 1,x 2) = x21 +2x 2. Remark 2. But not any restriction to a starlike set of a File Size: KB.A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator.

Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables. Tu, Zhenhan / Xiong, Liangpeng Page Published Online: 07/19/