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单纯形上的Stancu多项式与最佳多项式逼近 总被引:8,自引:2,他引:6
作为Bernstein多项式的推广,本文定义单纯形上的多元Stancu多项式.以最佳多项式逼近为度量,建立Stancu多项式对连续函数的逼近定理与逼近阶估计,给出Stancu多项式的一个逼近逆定理,从而用最佳多项式逼近刻划Stancu多项式的逼近特征. 相似文献
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In this paper we establish direct and inverse theorems for Stancu operator. Some other approximation properties of these operators are also given. 相似文献
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Grzegorz Nowak 《Journal of Mathematical Analysis and Applications》2009,350(1):50-55
In this paper, we introduce the generalized q-Bernstein polynomials based on the q-integers and we study approximation properties of these operators. In special case, we obtain Stancu operators or Phillips polynomials. 相似文献
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The purpose of this article is to give a Kantorovich generalization of Stancu type polynomials. We obtain convergence properties of our operators in the continuous function space and Lebesgue spaces. Furthermore, we get the order of approximation with the help of modulus of continuity and give a numerical example for approximation. 相似文献
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The present paper deals with the study of approximation by complex Stancu type generalization of Jakimovski–Leviatan type operators on a parabolic domain subset of complex plane by using the methods of Dressel et al. (Pacific J Math 13(4):1171–1180, 1963). 相似文献
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In this paper, the study of the problem of simultaneous approximation by the Szász–Mirakjan–Stancu–Durrmeyer type operators is carried out. An upper bound for the approximation to the rth-derivative of a function by these operators is established. 相似文献
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Octavian Agratini 《Central European Journal of Mathematics》2010,8(1):191-198
This paper is concerned with a generalization in q-Calculus of Stancu operators. Involving modulus of continuity and Lipschitz type maximal function, we give estimates for
the rate of convergence. A probabilistic approach is presented and approximation properties are established. 相似文献
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Octavian Agratini 《Chaos, solitons, and fractals》2011,44(11):977-981
Starting from a general sequence of linear and positive operators of discrete type, we associate its r-th order generalization. This construction involves high order derivatives of a signal and it looses the positivity property. Considering that the initial approximation process is A-statistically uniform convergent, we prove that the property is inherited by the new sequence. Also, our result includes information about the uniform convergence. Two applications in q-Calculus are presented. We study q-analogues both of Meyer-König and Zeller operators and Stancu operators. 相似文献
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本文定义了m维空间内一般单纯形上的Stancu算子,并给出了它对光滑函数的点态逼近误差的高阶渐近公式. 相似文献
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In this paper, we deal with the complex Baskakov-Szsz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR= {z ∈ C;|z| R}.Also, the exact order of approximation is found. The method used allows to construct complex Szsz-type and Baskakov-type approximation operators without involving the values on [0, ∞). 相似文献
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定义单纯形上高维Stancu算子的Boolean和迭代算子并且研究它逼近连续函数的正定理、逆定理与饱和定理,得到了较高的逼近阶. 相似文献
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The purpose of the paper is to introduce Stancu‐type linear positive operators generated by Dunkl generalization of exponential function. We present approximation properties with the help of well‐known Korovkin‐type theorem and weighted Korovkin‐type theorem and also acquire the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K‐functional, and second‐order modulus of continuity by Dunkl analogue of Szász operators. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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首先,引入一种由斜坡函数激发的神经网络算子,建立了其对连续函数逼近的正、逆定理,给出了其本质逼近阶.其次,引入这种神经网络算子的线性组合以提高逼近阶,并且研究了这种组合的同时逼近问题.最后,利用Steklov函数构造了一种新的神经网络算子,建立了其在L~p[a,b]空间逼近的正、逆定理. 相似文献
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In the present paper,the shape-preserving properties and the monotonicity for convex functions of Stancu operator are given.Moreover,the simultaneous approximation problems of this operator are also considered. 相似文献
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一类Bernstein型算子加权逼近 总被引:3,自引:1,他引:2
本文首先给出了一类用递归法定义的Bernsein型算子在一致逼近意义下的特征刻划,然后指出在通常的加权范数下,它虹无界的,通过引入的一种新范数,我们给出了该算子加Jacobi权逼近的特征刻划。 相似文献
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The purpose of the present paper is to introduce a Kantorovich modification of the q-analogue of the Stancu operators defined by Nowak (J Math Anal Appl 350:50–55, 2009). We study a local and a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness. Further A-statistical convergence properties of these operators are investigated. Next, a bivariate generalization of these operators is introduced and its rate of convergence is discussed with the aid of the partial and complete modulus of continuity and the Peetre‘s K-functional. 相似文献
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In the present paper, we deal with the complex Szász-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found. 相似文献