共查询到19条相似文献,搜索用时 250 毫秒
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刘国芬 《纯粹数学与应用数学》2014,(1):32-39
讨论Bernstein-Kantorovich算子的一种推广形式的逼近性质,运用插项的方法证明了逼近正定理,并证明了逆定理,得到了逼近等价定理.完善了算子在逼近性质方面的结果. 相似文献
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研究了指数有界的m次积分半群的离散逼近问题,利用可积的离散参数半群,获得了相关离散逼近结果.另外,给出了该逼近理论在非齐次抽象Cauchy问题中的应用. 相似文献
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本文研究多元有理逼近的Newman不等式与逼近逆定理问题.在多元Müntz多项式空间中利用分解方法建立多元有理多项式的Markov型不等式与Nikolskii型不等式.同时,建立多元有理逼近的逆定理,即Steckin型不等式.本文所获结果不仅推广了一元的相应结果,而且包含了关于代数多项式的一些经典结果. 相似文献
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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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前向神经网络的泛逼近性一直是神经网络的研究热点.本文给出了连续模糊函数的定义,依Hausdorff度量,借助模糊值Bernstein多项式关于连续模糊函数的逼近性质,证明了前向网络作为模糊函数泛逼近器的一致逼近性结果,并通过实例给出了逼近性的具体实现过程. 相似文献
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利用Ditzian-Totik光滑模,研究了推广的Kantorovich算子在Ba空间中的逼近,得到逼近的正定理与等价定理.所得结果改进、推广和统一了一些作者的结果. 相似文献
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构造了一类一致收敛于被逼近函数的多元序列,以此序列为基础,运用多元函数的全连续模及部分连续模来刻画这种多元推广的Bernstein算子的逼近性质,不仅得出了理论逼近结果,而且给出了数值逼近的例子. 相似文献
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本文在引进了推广的Kantorovich多项式算子的条件下,假设{αn}有界得到了该算子在逼近过程中的局部逆定理,从而推广了文献[1]中Z.Ditzian的结果. 相似文献
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本文在引进了推广的Kantorovich多项式算子的条件下,假设(an)有界得到了该算子在逼近过程中的局部逆定理,从而推广了文献「1」中Z-Ditzian的结果。 相似文献
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WANG XINGHUA 《数学年刊A辑(中文版)》1980,1(2):283-288
In a real or oompbx Banach space X, let P be an operator with Lipsohitz
continnous Frechet derivative P', and \[{X_*} \in X\] such that \[P({X_*}) = 0\] and \[{P^'}{({X_*})^{ - 1}}\] exists.
It is shown that a ball with center \[{X_*}\] and best possible radius such that the theorem of
Mysoyskich guarantees convergenee of Newton's method to \[{X_*}\] starting from any point
\[{x_0}\] in ihe ball (theorem 3). In comparison with the corresponding results of Rall's work
on Kantorovich theorem, the radius obtained is smaller than that from Kantorovich
theorem. Therefore we suggest here an improved form of Mysoyskich theorem (theorem
1) . Thus, the corresponding value of the radius is augmented beyond that from
Kantorovich theorem (theorem 2). 相似文献
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本文建立了拟模Abelian群上双参数算子族逼近的外推定理,所得的结果包含了DeVoreR.等人对正规逼近族之最佳逼近所建立的外推定理,且所需的条件更弱.同时从本文的结果立即可以建立起算子逼近的外推定理. 相似文献
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Some approximation results involving the q‐Szász–Mirakjan–Kantorovich type operators via Dunkl's generalization
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H. M. Srivastava M. Mursaleen Abdullah M. Alotaibi Md. Nasiruzzaman A. A. H. Al‐Abied 《Mathematical Methods in the Applied Sciences》2017,40(15):5437-5452
The purpose of this paper is to introduce a family of q‐Szász–Mirakjan–Kantorovich type positive linear operators that are generated by Dunkl's generalization of the exponential function. We present approximation properties with the help of well‐known Korovkin's theorem and determine the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K‐functional, and the second‐order modulus of continuity. Furthermore, we obtain the approximation results for bivariate q‐Szász–Mirakjan–Kantorovich type operators that are also generated by the aforementioned Dunkl generalization of the exponential function. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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M. Chen Y. Khan Q. Wu A. Yildirim 《Journal of Optimization Theory and Applications》2013,157(3):651-662
A Newton–Kantorovich convergence theorem of a modified Newton’s method having third order convergence is established under the gamma-condition in a Banach space to solve nonlinear equations. It is assumed that the nonlinear operator is twice Fréchet differentiable and satisfies the gamma-condition. We also present the error estimate to demonstrate the efficiency of our approach. A comparison of our numerical results with those obtained by other Newton–Kantorovich convergence theorems shows high accuracy of our results. 相似文献
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《Linear algebra and its applications》2001,322(1-3):19-41
We obtain a scalar inequality, converse to the Jensen inequality. We also derive an operator converse to the Jensen inequality. As special cases, we obtain inequalities, similar to the Kantorovich one as well as some operator generalizations of them. Using some exterior algebra, we prove a generalization of the Sylvester determinant theorem. We also deduce some determinant analogs of the additive and multiplicative Kantorovich inequalities. 相似文献
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The Kantorovich theorem is a fundamental tool in nonlinear analysis for proving the existence and uniqueness of solutions
of nonlinear equations arising in various fields. In the present paper we formulate and prove a generalized Kantorovich theorem
that contains as special cases the Kantorovich theorem and a weak Kantorovich theorem recently proved by Uko and Argyros.
An illustrative example is given to show that the new theorem is applicable in some situations in which the other two theorems
are not applicable. 相似文献