共查询到19条相似文献,搜索用时 93 毫秒
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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
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本文研究了推广的Roper-Suffridge算子保持一些双全纯映照子族的性质.利用一些双全纯映照子族的定义,得到了推广后的Roper-Suffridge算子在复Banach空间单位球上保持ρ次抛物形β型螺形映照及强α次殆星形映照的性质,由此得到复Hilbert空间上推广的Roper-Suffridge算子的相应性质,推广了已有的结论. 相似文献
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从定义出发证明复Banach空间特定域上推广的Roper-Suffridge算子保持α次强β型螺形性及ρ次抛物型β型螺形性,由此得到推广后的算子在复Banach空间特定域上保持α次强星形性、ρ次抛物星形性及抛物星形性,为由复平面C中单位圆盘D上的α次强β型螺形映照及ρ次抛物β型螺形映照来构造复Banach空间特定域上相应的映照提供了一种新的途径,充实了对Roper-Suffridge算子的研究. 相似文献
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张晓飞 《纯粹数学与应用数学》2023,(1):132-144
首先定义了一个新的螺形映射子族SB[β,A,B],其中■,-1≤BB[β,A,B]在复Banach空间单位球上的增长定理和沿某单位方向的偏差定理.最后给出了欧氏空间单位球Bn上正规化双全纯映射族成为SB[β,A,B]的充分条件.特别地,作为主要结果的应用,当β,A,B取某些特殊值时,可以很容易地得到一些熟知的结果. 相似文献
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在一般复Banach空间的单位球上引入正规化全纯映照族Mg,考虑满足条件(Df(x))-f(x)∈M9的正规化局部双全纯映照f(其中x=0是f(x)-x的k+1阶零点)并得到其增长和掩盖定理.所得结果统一和推广了许多已知结论. 相似文献
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LIU Hao LIU Ai-chao 《数学季刊》2005,20(4):331-337
Let f(x) be an almost spirallike mapping of type β with order B on unit ball B of complex Banach space X. In this paper, we consider the growth and covering theorems for f(x), we also prove that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known. 相似文献
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In this paper,we consider growth and covering theorem for f(x),where f(x) is spiallike mapping of typeβwith orderαdefined on unit ball B of complex Banach space, and x=0 is zero of order k+1 for f(x)-x.We also dicate that the estimation is precise whenβ=0 and still give growth upper bound and distortion upper hound for subordinate mapping.This result include some results known. 相似文献
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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
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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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在任意实Banach空间中引入了一对一致L-Lipschitz映象的具误差的新迭代序列,并证明了这些迭代序列的强收敛性定理.结果推广、完善和改进了最近的一些结果. 相似文献
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Let B be the unit ball in a complex Banach space. Let S^*k+1(B) be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k + 1 of f(z) - z. The authors obtain sharp growth and covering theorems, as well as sharp coefficient bounds for various subsets of S^*k+1(B). 相似文献
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曾六川 《数学物理学报(A辑)》2002,22(3):336-341
设犈是一致凸Banach空间,满足Opial条件或具有Frechet可微范数,犆是犈的非空闭凸子集,且犜:犆→犆是非扩张映象.又设对任何初始数据狓1 ∈犆,序列{狓狀}由下列修改了的Ishikawa迭代程序生成:狓狀+1 =狋狀犜狀(狊狀犜狀狓狀+ (1-狊狀)狓狀)+ (1-狋狀)狓狀, 狀≥1, (I)其中,数列{狋狀}与{狊狀}满足下列条件(i)和(ii)之一:(i)狋狀∈ [犪,犫]且狊狀∈ [0,犫];(ii)狋狀∈ [犪,1]且狊狀∈ [犪,犫],这里,常数犪,犫满足0<犪≤犫<1.作者证明了,犜有不动点的充要条件是,{狓狀}
弱收敛且{‖狓狀-犜狓狀‖}收敛到0.而且,由此即知,若犜有不动点,则{狓狀}弱收敛到犜的一个不动点. 相似文献
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Hemant Kumar Pathak 《Numerical Functional Analysis & Optimization》2018,39(4):449-466
A new 𝒮-generated Ishikawa iteration with errors is proposed for a pair of quasi-nonexpansive mapping and uniformly L-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. We show that the proposed iterative scheme converges strongly to a common solution of quasi-nonexpansive mapping and uniformly L-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. A comparison table is prepared using a numeric example which shows that the proposed iterative algorithm is faster than some known iterative algorithms. 相似文献
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一类多复变全纯映照子族的增长和偏差定理 总被引:1,自引:0,他引:1
在一般复Banach空间X中的单位球B上引入一类全纯映照族M_g.考虑B上满足条件(Df(x))~(-1)f(x)∈M_g的正规化局部双全纯映照f(x)(其中x=0是f(x)-x的k+1阶零点)并得到其增长定理.作为应用,也得到了C~n中单位多圆柱D~n上映照f关于Jacobi矩阵Jf(z)的偏差定理,该结果统一和推广了星形映照许多子族的相应结论. 相似文献
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Ian Graham Hidetaka Hamada Gabriela Kohr Mirela Kohr 《Complex Analysis and Operator Theory》2013,7(6):1909-1927
In this paper we consider the notion of asymptotic spirallikeness in reflexive complex Banach spaces $X$ , and the connection with univalent subordination chains. Poreda initially introduced the notion of asymptotic starlikeness to characterize biholomorphic mappings on the unit polydisc in $\mathbb{C }^{n}$ which have parametric representation in the sense of Loewner theory. The authors introduced the notions of $A$ -asymptotic spirallikeness and $A$ -parametric representation on the Euclidean unit ball of $\mathbb{C }^{n}$ , where $A\in L(\mathbb{C }^{n})$ with $m(A)>0$ . They showed that these notions are equivalent whenever $k_+(A)<2m(A)$ . In this paper we prove that if $k_+(A)<2m(A)$ and $f\in S(B)$ has $A$ -parametric representation, then $f$ is also $A$ -asymptotically spirallike on the unit ball $B$ of $X$ . For the converse, we need the additional assumption that $f$ is a smooth $A$ -asymptotically spirallike mapping, except in the finite-dimensional case $X=\mathbb{C }^{n}$ with an arbitrary norm. The notion of asymptotic spirallikeness involves differential equations and may be regarded as giving a geometric characterization of certain domains in $X$ . That is one of the motivations for considering this notion in the case of reflexive complex Banach spaces. 相似文献