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61.
In this paper, we obtain a distortion theorem of Jacobian matrix for biholomorphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of starlike mappings to higher dimensions. We then give an upper bound estimate for biholomorphic subclasses of starlike mappings along a unit direction in a complex Banach space. 相似文献
62.
对α次的殆β型螺形映射,α次的β型螺形映射和α次的强β型螺形映射,给出了定义,并且在复Banach空间中的单位球上分别得到它们的增长掩盖定理. 相似文献
63.
Bohr's type inequalities are studied in this paper: if f is a holomorphic mapping from the unit ball B~n to B~n, f(0)=p, then we have sum from k=0 to∞|Dφ_P(P)[D~kf(0)(z~k)]|/k!||Dφ_P(P)||<1 for|z|<max{1/2 |P|,(1-|p|)/2~(1/2)andφ_P∈Aut(B~n) such thatφ_(p)=0. As corollaries of the above estimate, we obtain some sharp Bohr's type modulus inequalities. In particular, when n=1 and |P|→1, then our theorem reduces to a classical result of Bohr. 相似文献
64.
本文分别讨论Cn中某一Reinhardt域上以及复Hilbert空间单位球上推广的Roper-Suffridge算子保持α(-π/2<α<π/2)型螺形性和保持α(0<α<1)次星形性.所得结果包含了已知对应的结论. 相似文献
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66.
本文分别讨论Cn中某一Reinhardt域上以及复Hilbert空间单位球上推广的Roper-Suffridge算子保持α(-π/2<α<π/2)型螺形性和保持α(0<α<1)次星形性.所得结果包含了已知对应的结论. 相似文献
67.
关于局部双全纯映射的推广的Roper-Suffridge算子 总被引:15,自引:4,他引:11
§ 1. Introduction LetUbetheunitdiskinCandBnbetheunitballinCn.In 1 995 ,RoperandSuffridgeintroducedanextensionoperator.ThisoperatorisdefinedforanormalizedlocallybiholomorphicfunctionfonUbyΦn(f) (z) =F(z) =(f(z1 ) ,f′(z1 )z′) ,z =(z1 ,z′)∈Bn,(1 .1 )wherez1 ∈U ,z′=(z2 ,… ,zn)∈Cn- 1 ,andthebranchofthesquarerootischosensuchthatf′(0 ) =1 .TheRoper Suffridgeextensionoperatorhasthefollowingimportantproperties:(a)IffisanormalizedconvexfunctiononU ,thenFisanormalizedconvexmappingon… 相似文献
68.
本文考虑一般复Banach空间中单位球上和Cn中单位多圆柱上的正规化双全纯α(-π/2<α<π/2)型螺形映照f(其中x=0是f(x)-x的k+1阶零点),研究了它的构造,并得到其精细的增长、掩盖定理以及齐次展开式的精细估计.所得的结果包含了许多已知的结论. 相似文献
69.
对Cn中某一Reinhardt域上以及复Hilbert空间单位球上推广的Roper-Suffridge算子保持α(0《α《1)次的β(-π/2《β《π/2)型螺形性进行了讨论.所得的结果推广了以前相应的结论. 相似文献
70.
A class of biholomorphic mappings named “quasi-convex mapping” is introduced in the unit ball of a complex Banach space. It
is proved that this class of mappings is a proper subset of the class of starlike mappings and contains the class of convex
mappings properly, and it has the same growth and covering theorems as the convex mappings. Furthermore, when the Banach space
is confined to ℂn, the “quasi-convex mapping” is exactly the “quasi-convex mapping of type A” introduced by K. A. Roper and T. J. Suffridge. 相似文献