共查询到19条相似文献,搜索用时 93 毫秒
1.
丁春梅 《数学物理学报(A辑)》2010,30(1):142-153
该文证明了C[0,1]空间中的函数及其导数可以用Bernstein算子的线性组合同时逼近,得到逼近的正定理与逆定理.同时,也证明了Bernstein算子导数与函数光滑性之间的一个等价关系.该文所获结果沟通了Bernstein算子同时逼近的整体结果与经典的点态结果之间的关系. 相似文献
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借助光滑模ω_φ~2(f,t)(φ是一般步权函数),研究了Bernstein算子的点态同时逼近问题,给出了Bernstein算子同时逼近的等价定理,建立了其导数与光滑函数间的关系,对以前已有的结果予以补充和完善. 相似文献
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单纯形上的Bernstein多项式 总被引:5,自引:0,他引:5
本文研究了单纯形上的Bernstein多项式的一系列性质.我们给出了Bernstein多项式逼近连续函数的精确误差界,确定了Bernstein多项式的最佳逼近度,并得到了Bernstein算子及其逆算子的渐近展开式.最后,这些结果被应用于单纯形上Bezier网的研究. 相似文献
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某些正线性算子对有界变差函数的点态逼近度 总被引:5,自引:0,他引:5
1 引言 R.Bojanic在文献[1]研中究了Fourier算子对有界变差函数的点态逼近度,1983年Cheng Fuhua在他的博士论文中研究了Bernstein算子对BV函数的点态逼近度。本文将给出一般正线性算子对有界变差函数的点态逼近度。作为例子,我们给出Bernstein算子和Kantorovitch算子对有界变差函数的点态逼近度。应当指出,文献[2] 相似文献
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本文利用加权Ditzian-Totik光滑模证明Bernstein型算子的线性组合加权逼近阶估计和等价定理;同时,研究加Jacobi权下Benstein型算子的高阶导数与所逼近函数光滑性之间的关系. 相似文献
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借助于光滑模ωψ^rλ(f,t)(0≤λ≤1)给出了Bernstein算子线性组合同时逼近的点态结果。 相似文献
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给出了一类用广义杨辉三角阵定义的Bernstein型算子线性组合加Ja-cob i权的逼近在一致逼近意义下的特征刻划. 相似文献
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讨论了修正的 Durrmeyer- Bernstein算子线性组合的一致逼近问题 ,给出了正定理、逆定理和特征刻划 . 相似文献
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In the present note we prove general asymptotic and Voronovskaya theorems for simultaneous approximation. These generalize
the Voronovskaya type theorems obtained recently by Floater for the Bernstein operators, and previously by Heilmann and Müller
for the Durrmeyer operators. 相似文献
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A.J.?Lpez-Moreno 《Acta Mathematica Hungarica》2005,106(4):343-354
Summary We obtain preservation inequalities for Lipschitz constants of higher order in simultaneous approximation processes by Bernstein type operators. From such inequalities we derive the preservation of the corresponding Lipschitz spaces. 相似文献
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Summary We obtain preservation inequalities for Lipschitz constants of higher order in simultaneous approximation processes by Bernstein type operators. From such inequalities we derive the preservation of the corresponding Lipschitz spaces. 相似文献
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We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators
of S.N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating
our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates
for simultaneous approximation of derivatives are given. 相似文献
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Nursel etin 《Mathematical Methods in the Applied Sciences》2019,42(16):5582-5594
In this paper, we investigate approximation properties of the complex form of an extension of the Bernstein polynomials, defined by Stancu by means of a probabilistic method. We obtain quantitative upper estimates for simultaneous approximation and the exact order of approximation by these operators attached to analytic functions in closed disks. Also, we prove that the new generalized complex Stancu operators preserve the univalence, starlikeness, convexity, and spirallikeness in the unit disk. 相似文献
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Our results describe how quantitative properties of univariate operators are inherited by the tensor product of their parametric extensions. This includes statements concerning simultaneous approximation. The estimates are in terms of partial and total moduli of smoothness of higher order. Applications are given for cubic interpolatory splines and Bernstein operators. Further applications are possible. 相似文献
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The present paper deals with the study of the rate of convergence of the Bézier variant of certain Bernstein Durrmeyer type operators in simultaneous approximation. 相似文献
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In this work we discuss the rate of simultaneous approximation of Hölder continuous functions by Bernstein operators, measured by Hölder norms with different exponents. We extend the known results on this topic. 相似文献
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Borislav R. Draganov 《Results in Mathematics》2014,66(1-2):21-41
The paper presents upper estimates of the error of weighted and unweighted simultaneous approximation by the Bernstein operators and their iterated Boolean sums. The estimates are stated in terms of the Ditzian–Totik modulus of smoothness or appropriate K-functionals. 相似文献