共查询到10条相似文献,搜索用时 78 毫秒
1.
Chen Zhiguo 《Israel Journal of Mathematics》2001,122(1):347-358
In the theory ofK-quasiconformal mappings, Mori's theorem shows thatK-quasiconformal mappings on the unit disk satisfy the Hölder condition, where the coefficient 16 is best possible. In this paper, we prove that self-μ(z)-homeomorphisms on the unit disk have an analogical result to Mori's theorem when the integral mean dilatations are controlled by log function. An unimprovable inequality is obtained. 相似文献
2.
3.
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to ℂ
n
, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems
of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order
α defined on the polydisc in ℂ
n
and on the unit ball in a complex Banach space, respectively.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
4.
Xiaohui Zhang Gendi Wang Songliang Qiu 《Journal of Mathematical Analysis and Applications》2006,324(1):60-65
The authors prove a conjecture on elliptic integrals and obtain sharp bounds for φK(r) and λ(K). By using Teichmüller's module theorem, the authors obtain a distortion theorem of K-quasiconformal mappings on the plane. 相似文献
5.
复Banach空间中单位球上双全纯凸映射的偏差定理 总被引:1,自引:0,他引:1
本文讨论一般复Banach空间上单位球B的Caratheodory度量和Kobayashi 度量的性质,并据此将Cn(n≥1)中单位球Bn上双全纯凸映射的矩阵形式偏差定理 推广到一般复Banach空间的单位球B上. 相似文献
6.
Irwin Kra 《Israel Journal of Mathematics》1978,30(1-2):152-158
Teichmüller’s theorem gives necessary and sufficient conditions for mapping one ordered quadruple by aK-quasiconformal map onto a second ordered quadruple. We give a simple non-computational proof of the necessity part. We then
characterize such extremal mappings, and obtain as a consequence a new formula for the modular function, with leads to a very
simple derivation of the known expression for the Poincaré metric on the thrice-punctured sphere.
Research partially supported by NSF grant MCS 76-04969A01. 相似文献
7.
Asrifa Sultana 《Numerical Functional Analysis & Optimization》2017,38(8):1060-1068
In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky–Rivlin theorem on iterates of the Bernstein operators on C[0,1]. 相似文献
8.
LIU Taishun & XU Qinghua Department of Mathematics Huzhou Teachers College Huzhou China Department of Mathematics Jiangxi Normal University Nanchang China 《中国科学A辑(英文版)》2006,(11)
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively. 相似文献
9.
Mark Elin 《Journal of Mathematical Analysis and Applications》2011,377(1):239-250
The Roper-Suffridge extension operator and its modifications are powerful tools to construct biholomorphic mappings with special geometric properties. The first purpose of this paper is to analyze common properties of different extension operators and to define an extension operator for biholomorphic mappings on the open unit ball of an arbitrary complex Banach space. The second purpose is to study extension operators for starlike, spirallike and convex in one direction mappings. In particular, we show that the extension of each spirallike mapping is A-spirallike for a variety of linear operators A. Our approach is based on a connection of special classes of biholomorphic mappings defined on the open unit ball of a complex Banach space with semigroups acting on this ball. 相似文献
10.
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings.Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space Ⅹ. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order α defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively. 相似文献