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Articles

Distortion results for a certain subclass of biholomorphic mappings in ℂn

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Pages 887-897 | Received 20 Dec 2019, Accepted 01 Nov 2020, Published online: 06 Dec 2020

References

  • Duren PL. Univalent functions. New York (NY): Springer-Verlag; 1983. (Grundlehren der mathematischen Wtssenschaften; 259).
  • Cartan H. Sur la possibilité détendre aux fonctions de plusieurs variables complexes la théorie des fonctions univalentes. In: Montel P, editor. Lecons sur les Fonctions Univalentes ou Multivalentes. Paris: Gauthier-Villars; 1933.
  • Chu CH, Hamada H, Honda T, et al. Distortion of locally biholomorphic Bloch mappings on bounded symmetric domains. J Math Anal Appl. 2016;441(2):830–843.
  • Graham I, Hamada H, Kohr G. Parametric representation of univalent mappings in several complex variables. Can J Math. 2002;54(2):324–351.
  • Graham I, Hamada H, Kohr G. Loewner chains, Bloch mappings and Pfaltzgraff-Suffridge extension operators on bounded symmetric domains. Complex Var Elliptic Equ. 2020;65(1):57–73.
  • Hamada H, Honda T, Kohr G. Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation. J Math Anal Appl. 2006;317(1):302–319.
  • Wang JF. Distortion theorem for locally biholomorphic Bloch mappings on the unit ball Bn. Bull Malaysian Math Sci Soc. 2015;38(4):1657–1667.
  • Barnard R, FitzGerald C, Gong S. A distortion theorem for biholomorphic mappings in C2. Trans Am Math Soc. 1994;344:907–924.
  • Chu CH, Hamada H, Honda T, et al. Distortion theorems for convex mappings on homogeneous balls. J Math Anal Appl. 2010;369(2):437–442.
  • Gong S, Wang SK, Yu QH. Biholomorphic convex mappings of ball in Cn. Pac J Math. 1993;161(2):287–306.
  • Gong S, Liu TS. Distortion theorems for biholomorphic convex mappings on bounded convex circular domains. Chin Ann Math Ser B. 1999;20(03):297–304.
  • Xu QH, Liu TS. Sharp growth and distortion theorems for a subclass of biholomorphic mappings. Comput Math Appl. 2010;59(12):3778–3784.
  • Zhu YC, Liu MS. Distortion theorems for biholomorphic convex mappings in Banach spaces. Complex Var. Theory Appl. 2005;50:57–68.
  • Liu TS, Wang JF, Lu J. Distortion theorems of starlike mappings in several complex variables. Taiwan J Math. 2011;15(6):2601–2608.
  • Liu XS, Liu TS. Sharp distortion theorems for a subclass of biholomorphic mappings which have a parametric representation in several complex variables. Chin Ann Math. 2016;37(4):553–570.
  • Tu ZH, Xiong LP. Growth and distortion results for a class of biholomorphic mapping and extremal problem with parametric representation in Cn. Complex Anal Oper Theory. 2019;13(6):2747–2769.
  • Xu QH, Liu TS. On the growth and covering theorem for normalized biholomorphic mappings. Chin Ann Math. 2009;30(A):213–220.

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