THE GROWTH THEOREM FOR -FOLD SYMMETRIC CONVEX MAPPINGS

TATSUHIRO HONDA

doi:10.1112/S0024609302001388

Abstract

In this paper, a growth result is obtained for normalized $k$ -fold symmetric convex biholomorphic mappings on the unit ball of a complex Banach space.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Liu, Taishun and Liu, Xiaosong 2004. On the precise growth, covering, and distortion theorems for normalized biholomorphic mappings. Journal of Mathematical Analysis and Applications, Vol. 295, Issue. 2, p. 404.

Hamada, Hidetaka Honda, Tatsuhiro and Kohr, Gabriela 2006. Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation. Journal of Mathematical Analysis and Applications, Vol. 317, Issue. 1, p. 302.

Xiaosong, Liu and Taishun, Liu 2007. On the sharp growth, covering theorems for normalized biholomorphic mappings in n. Acta Mathematica Scientia, Vol. 27, Issue. 4, p. 803.

Hamada, Hidetaka and Honda, Tatsuhiro 2008. Sharp growth theorems and coefficient bounds for starlike mappings in several complex variables. Chinese Annals of Mathematics, Series B, Vol. 29, Issue. 4, p. 353.

Liu, Xiao-Song and Liu, Ming-Sheng 2010. Quasi-convex mappings of order $\alpha$ on the unit polydisk in $C^n$. Rocky Mountain Journal of Mathematics, Vol. 40, Issue. 5,

Liu, Xiaosong and Liu, Taishun 2011. The sharp estimates of all homogeneous expansions for a class of quasi-convex mappings on the unit polydisk in ℂ n. Chinese Annals of Mathematics, Series B, Vol. 32, Issue. 2, p. 241.

Wang, Jianfei Liu, Taishun and Lu, Jin 2011. Growth and distortion theorems on subclasses of quasi-convex mappings in several complex variables. Frontiers of Mathematics in China, Vol. 6, Issue. 5, p. 931.

Xu, Qinghua Liu, Taishun and Liu, Xiaosong 2012. The sharp estimates of homogeneous expansions for the generalized class of close-to-quasi-convex mappings. Journal of Mathematical Analysis and Applications, Vol. 389, Issue. 2, p. 781.

Cui, Yan-Yan Wang, Chao-Jun and Zhu, Si-Feng 2014. Growth Theorems for a Subclass of Strongly Spirallike Functions. Journal of Applied Mathematics, Vol. 2014, Issue. , p. 1.

Liu, XiaoSong Liu, TaiShun and Xu, QingHua 2015. A proof of a weak version of the Bieberbach conjecture in several complex variables. Science China Mathematics, Vol. 58, Issue. 12, p. 2531.

Liu, Xiao-song and Liu, Tai-shun 2016. Sharp distortion theorems for a subclass of quasi-convex mappings in several complex variables. Complex Variables and Elliptic Equations, Vol. 61, Issue. 3, p. 359.

LIU, Xiaosong and LIU, Taishun 2016. Sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of typeBand order α in several complex variables. Acta Mathematica Scientia, Vol. 36, Issue. 6, p. 1808.

Liu, Xiaosong and Liu, Taishun 2016. Sharp distortion theorems for a subclass of biholomorphic mappings which have a parametric representation in several complex variables. Chinese Annals of Mathematics, Series B, Vol. 37, Issue. 4, p. 553.

Liu, Xiaosong and Liu, Taishun 2021. On the Refined Esitmates of All Homogeneous Expansions for a Subclass of Biholomorphic Starlike Mappings in Several Complex Variables. Chinese Annals of Mathematics, Series B, Vol. 42, Issue. 6, p. 909.

Liu, Xiaosong Liu, Taishun and Zhang, Wenjun 2021. The sharp estimates of main coefficients for starlike mappings in ℂn. Complex Variables and Elliptic Equations, Vol. 66, Issue. 10, p. 1782.

Xiong, Liangpeng Xiong, Junzhou and Zhang, Ruyu 2024. Some results of quasi-convex mappings which have a $$\varvec{\Phi }$$-parametric representation in higher dimensions. Analysis and Mathematical Physics, Vol. 14, Issue. 3,

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THE GROWTH THEOREM FOR $k$-FOLD SYMMETRIC CONVEX MAPPINGS

Abstract

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THE GROWTH THEOREM FOR $k$-FOLD SYMMETRIC CONVEX MAPPINGS

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