单位球上α次准凸映射精细的偏差定理
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摘要
利用欧氏空间单位球的边界型Schwarz引理给出α次准凸映射在极值点处精细的行列式型偏差定理和矩阵型偏差定理.
In this article,we obtained the sharp distortion theorems of determinant and sharp distortion theorems of matrix at the extreme points for quasi-convex mapping of orderα using the Schwarz lemma at the boundary of unit ball in Euclidean space.
In this article,we obtained the sharp distortion theorems of determinant and sharp distortion theorems of matrix at the extreme points for quasi-convex mapping of orderα using the Schwarz lemma at the boundary of unit ball in Euclidean space.
引文
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[7]Graham I,Kohr G.Geometric function theory in one and higher dimensions[M].New York:Marcel Dekker,2003.
[8]Chu C H,Hamada H,Honda T,Kohr G.Distortion theorems for convex mappings on homogeneous balls[J].J Math Anal Appl,2010,369:437-442.
[9]Zhang X F,Liu T S,Lu J.The growth,covering and distortion theorems for a subclass of convex mappings[J].Complex Variables and Elliptic Equations,2015,60(6):787-800.
[10]Roper K A,Suffridge T J.Convexity properties of holomorphic mappings in C~n[J].Trans Amer Math Soc,1999,351:1803-1833.
[11]刘太顺,刘浩.有界凸圆型域上的准凸映照[J].数学学报,2001,44(2):287-292.
[12]刘太顺,张文俊.复Banach空间单位球上准凸映射的增长定理和掩盖定理[J].中国科学,2002,32(11):1033-1041.
[13]Liu T S,Xu Q H.On quasi-convex mappings of order a in the unit ball of a complex Banach space[J].Sci China Math,2006,49(11):1451-1457.
[14]林运泳,洪毅.Banach空间中全纯映射的若干性质[J].数学学报,1995,38(2):234-241.
[15]Liu T S,Wang J F,Tang X M.Schwarz lemma at the boundary of the unit ball in C~n and its application[J].J Geom Anal,2015,25:1890-1914.
[16]Wang J F,Liu T S,Lu J.Growth and distortion theorems on subclasses of quasi-convex mappings in several complex variables[J].Font Math China,2011,6(5):931-944.
[17]Zhang X F,Liu T S,Xie Y H.Distortion theorems for normalized biholomorphic qua si-convex mappings[J].Acta Math Sinica,2017,33(9):1242-1248.
[2]Barnard R W,Fitzgerald C H,Gong S.Distortion theorem for biholomorphic mappings in C~2[J].Trans Amer Math Soc,1994,344:907-924.
[3]刘太顺,张文俊.C~n中双全纯凸映射的偏差定理[J].数学年刊,1999,20(4):505-512.
[4]Gong S,Wang S K,Yu Q H.Biholomorphic convex mappings of ball in C~n[J].Pac J Math,1993,161(2):287-306.
[5]Gong S,Liu T S.Distortion theorems for biholomorphic convex mappings on bounded circular convex domains.Chin.Ann.Math.,1999,20(3):297-304.
[6]刘太顺,张文俊.复Banach空间中单位球上双全纯凸映射的偏差定理[J].数学学报,2003,46(6):1041-1046.
[7]Graham I,Kohr G.Geometric function theory in one and higher dimensions[M].New York:Marcel Dekker,2003.
[8]Chu C H,Hamada H,Honda T,Kohr G.Distortion theorems for convex mappings on homogeneous balls[J].J Math Anal Appl,2010,369:437-442.
[9]Zhang X F,Liu T S,Lu J.The growth,covering and distortion theorems for a subclass of convex mappings[J].Complex Variables and Elliptic Equations,2015,60(6):787-800.
[10]Roper K A,Suffridge T J.Convexity properties of holomorphic mappings in C~n[J].Trans Amer Math Soc,1999,351:1803-1833.
[11]刘太顺,刘浩.有界凸圆型域上的准凸映照[J].数学学报,2001,44(2):287-292.
[12]刘太顺,张文俊.复Banach空间单位球上准凸映射的增长定理和掩盖定理[J].中国科学,2002,32(11):1033-1041.
[13]Liu T S,Xu Q H.On quasi-convex mappings of order a in the unit ball of a complex Banach space[J].Sci China Math,2006,49(11):1451-1457.
[14]林运泳,洪毅.Banach空间中全纯映射的若干性质[J].数学学报,1995,38(2):234-241.
[15]Liu T S,Wang J F,Tang X M.Schwarz lemma at the boundary of the unit ball in C~n and its application[J].J Geom Anal,2015,25:1890-1914.
[16]Wang J F,Liu T S,Lu J.Growth and distortion theorems on subclasses of quasi-convex mappings in several complex variables[J].Font Math China,2011,6(5):931-944.
[17]Zhang X F,Liu T S,Xie Y H.Distortion theorems for normalized biholomorphic qua si-convex mappings[J].Acta Math Sinica,2017,33(9):1242-1248.