共查询到19条相似文献,搜索用时 78 毫秒
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有界正则函数的导数估计 总被引:2,自引:0,他引:2
在这篇文章中,主要讨论了n阶导数的估计式,即对有界正则函数φ(z)=c0 c1z … cnz^n …(在│z│1内正则),从已知的三阶、四阶导数估计式,利用归纳法原理及有界正则函数的性质推出n阶导数的一般估计式,并推出在│z│<1内正则的正实部函数的n阶导数的一般估计式。 相似文献
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讨论了系数是单位圆内解析函数的二阶齐次和非齐次线性微分方程的解及其一阶导数和二阶导数与小函数之间的关系,并得到了它们之间的精确估计. 相似文献
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研究了单位开圆盘内保向复值的调和函数类,其中函数的解析部分满足一定的从属条件.完整的给出了该函数类Bloch常数的界、系数估计、增长和偏差不等式的界.进一步,通过指定一些关键参数,证明其pre-Schwarzian导数的范数也是有界的. 相似文献
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讨论了正则的正实部函数的导数估计问题,利用正实部函数的性质,得到三阶导数、四阶导数的准确估计式. 相似文献
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给出了从典型域到单位球的全纯映射高阶Frchet导数的Schwarz-Pick估计,从而推广了单位球上全纯自映射Frchet导数的Schwarz-Pick估计以及单位圆盘上有界全纯函数高阶导数的Schwarz-Pick估计的结论. 相似文献
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研究了一类n阶可微函数,利用其n阶导数上、下界以及Cruis不等式,给出了n阶可微函数Ostrowski型不等式,从而推广二阶可微函数Ostrowski型不等式. 相似文献
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本文通过研究几种特殊类型函数的高阶导数与原函数的求法 ,获得了由该类函数自身及其一阶导数的特征 ,即可快速写出该类函数的 n阶导数 y( n) 与原函数 y( - 1 ) 的统一公式 y( n) ( n=-1 ,1 ,2 ,3 ,… ) .该公式可给实际运算带来许多简化与方便 . 相似文献
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In this note we consider higher order derivatives of bounded analytic functions.
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Boo Rim Choe Hyungwoon Koo Wayne Smith 《Transactions of the American Mathematical Society》2003,355(7):2829-2855
We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.
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Vijay Gupta 《Annali dell'Universita di Ferrara》2013,59(2):311-318
In the present article we find the hypergeometric representation of the Szász-Beta operators and obtain the moments using confluent hypergeometric functions, which can be related to generalized Laguerre polynomials. Then we estimate a convergence result for functions having bounded derivatives. 相似文献
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本文主要得到亚纯函数与它们的n阶导数分担某些值时的唯一性的一个一般性定理,推广和改进了Shibazki.仪洪勋等人的某些结果。 相似文献
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We apply the capacity and symmetrization methods to distortion theorems for analytic functions in an annulus. We show that the classical Teichmüller estimate for the capacity of a doubly-connected domain yields a series of the already known and new inequalities for univalent functions. In particular, we supplement the results of Grötzsch, Duren, and Huckemann. Using the dissymmetrization of condensers we establish sharp estimates for local distortion and the distortion of level curves in n ≥ 2 symmetric directions. In terms of Robin functions we give an analog of the Nehari inequality: some general distortion theorem for several points taking into account the boundary behavior of the function and describing the cases of equalities. As a corollary we give analogs of some inequalities of Solynin, Pommerenke, and Vasil’ev that were obtained previously for univalent and bounded functions in a disk. We prove a distortion theorem that involves the Schwarzian derivatives at symmetric points on the unit circle. 相似文献
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Seiki MORI 《数学季刊》2005,20(3):226-231
In this paper, we consider the problem of the uniqueness for meromorphic functions whose n-th derivatives share the same 1-points. The results in this paper are different from all of theorems given by H X Yi and C C Yang and other authors. 相似文献
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We estimate pointwise convergence rates of approximation for functions with derivatives of bounded variation and for functions which are exponentially bounded and have derivatives locally of bounded variation. The approximation is made through the operation of a sequence of integral operators with not necessarily positive kernel functions. The general result is then applied to deduce estimates for Beta operators, Hermite-Fejér operators, Picard operators, Gauss-Weierstrass operators, Baskakov operators, Mirakjan-Szász operators, Bleimann-Butzer-Hahn operators, Phillips operators, and Post-Widder operators. 相似文献