二元Baskakov算子的逼近

在［１］中构造了一系列一元及多元线性算子，其中包括二元Ｂａｓｋａｋｏｖ算子，本文讨论该算子在Ｃ空间的逼近性质．     

关于多元Baskakov算子的加权逼近

本文首先指出一类多元Ｂａｓｋａｋｏｖ算子在通常的加权范数下是无界的．然后给出了一类新的加权范数,在此范数下它是压缩的．最后利用多元分解技巧,解决了多元Ｂａｓｋａｋｏｖ算子加权逼近的特征刻划文问题．     

二元非乘积型Baskakov算子的某些逼近性质

该文利用多元分解技巧及一元的结果得出二元非乘积型算子V\-n的两个逼近性质定理.对f∈C\-0(T\+2),‖V\-n(f)-f‖≤cω\-2(f,[SX(]1[]n[SX)]); 对f∈C\+2(T\+2),lim[DD(X]n→∞[DD)]n(V\-n(f)-f)=[SX(]x(1+x)[]2[SX)]f\-\{11\}+[SX(]y(1+y)[]2[SX)]f\-\{22\}+[SX(]xy[]2[SX)]f\-\{12\}.     

Approximation Properties For Modified q-Bernstein-Kantorovich Operators

The purpose of this article is to give a generalization of q-Bernstein-Kantorovich operators. We present some approximation theorems. We compute the rate of convergence and error estimation of these operators by means of the modulus of continuity. Furthermore, we give some numerical examples to show comparisons in illustrative graphics for the convergence of these operators to various functions.     

Pointwise Simultaneous Approximation by Combinations of Baskakov Operators

In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators.     

Baskakov算子线性组合同时逼近的等价定理

本文建立了Baskakov算子线性组合同时逼近的等价定理。     

On the Rate of Convergence for Modified Baskakov Operators

We consider some linear operators in certain weighted spaces of functions of one variable and study approximation properties of these operators. The method was inspired by Kirov [4].     

修正的Bernstein-Durrmeyer算子的同时逼近

本文的目的是证明修正的Bernstein-Durrmeyer算子同时逼近的正逆定理,在点态意义下,我们得到了一个同时逼近的等价特征刻画。     

Approximation Properties by q-Durrmeyer-Stancu Operators

In this paper, we are dealing with q-Bemstein-Durrmeyer-Stancu operators. Firstly, we have estimated moments of these operators. Then we have discussed some approximation properties and asymptotic formulas. We have obtained better estimations by using King type approach and given statistical convergence for the operators.     

Approximation Properties of Two-Dimensional q-Bernstein-Chlodowsky-Durrmeyer Operators

This article deals with the Durrmeyer-type generalization of the q-Bernstein-Chlodowsky operators on a rectangular domain (which were introduced by Büyükyaz?c? [2 ?. Büyükyaz?c? ( 2009 ). On the approximation properties of two-dimensional q-Bernstein-Chlodowsky polynomials . Math. Commun. 14 : 255 – 269 .[Web of Science ®] , [Google Scholar]]). We obtain the Korovkin-type approximation properties and the rates of convergence of this generalization using the means of the modulus of continuity and using the K-functional of Peetre. Further, we establish the weighted approximation properties for these operators.     

Pointwise Estimate for Baskakov Operators

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｆｏｒｔｈｅｗｅｌｌ ｋｎｏｗｎＢｅｒｎｓｔｅｉｎｐｏｌｙｎｏｍｉａｌＢｎ(ｆ;ｘ) = ｎｋ=0ｆ ｋｎ ｐｎ,ｋ(ｘ) ,　ｐｎ ,ｋ(ｘ) =ｎｋ ｘｋ( 1 -ｘ) ｎ-ｋ,ＢｅｒｅｎｓａｎｄＬｏｒｅｎｔｚ[1]ｐｒｏｖｅｄｔｈａｔｆｏｒｆ∈Ｃ[0 ,1 ] ,0 <α<2 ,ｏｎｅｈａｓ｜ (Ｂｎｆ-ｆ) (ｘ) ｜=Ｏ ｘ( 1 -ｘ)ｎα/ 2 ω2 (ｆ;ｔ) =Ｏ(ｔα) . ( 1 .1 )Ｏｎｔｈｅｏｔｈｅｒｈａｎｄ ,ＤｉｔｚｉａｎａｎｄＴｏｔｉｋ[2 ]ｏｂｔａｉｎｅｄｔｈａｔｆｏｒｆ∈Ｃ[0 ,1 ] ,0 <α<2 ,ｏｎｅｈａｓ｜ (Ｂｎｆ -ｆ)…     

双截断Baskakov局部化算子的收敛性

本文考虑Baskakov算子的一种新的局部化算子,获得了该算子的一些收敛性质.另外,利用概率论中心极限定理,建立了Baskakov算子核的新估计.     

Baskakov算子线性组合加Jacobi权逼近及高阶导数的正逆定理

利用加权光滑模ωrψλ(f,t)ω给出了Baskakov算子的线性组合加Jacobi权逼近的正逆定理;另外,研究了加Jacobi权下Baskakov算子的高阶导数与所逼近函数光滑性之间的关系.     

Approximation Properties and Some Classes of Operators

The following questions and close problems are studied.(i) Is it true that T is p-nuclear provided that T ^** is p-nuclear? (ii) Is it true that Tis dually p-nuclear provided that T ^* is p-nuclear? (iii) Is it true that if T ^*is compactly factorable in the space l _p, then T is (strictly) factorable in the space l _p'? Here, T ^* is the adjoint operator of a bounded operator T:X Yin Banach spaces X and Y. Bibliography: 30 titles.     

Approximation Properties of Recursively Defined Bernstein-Type Operators

We consider a generalization of classical Bernstein operators obtained by replacing the binomial coefficients with general ones satisfying a suitable recursive relation. We study the uniform convergence of these operators together with some quantitative estimates and regularity properties. Finally, in some particular cases, we investigate the behavior of the iterates.     

On Approximation Properties of Generalized q-Bernstein Operators

In this study, we identify a generalization of q-Bernstein type operators and investigate approximation properties of a sequence of these operators . We estimate rate of approximation by modulus of continuity. We prove Voronovskaya type theorem for these operators.     

模糊粗糙近似算子的拓扑性质

考虑论域上一二元关系所决定的模糊粗糙近似算子的拓扑性质,证明了任一自反二元关系可以决定一模糊拓扑.并且,当二元关系自反对称时,该模糊拓扑中的元是开集当且仅当它是闭集;当二元关系自反传递时,该模糊拓扑的闭包与内部算子恰为模糊粗糙上、下近似算子.     

Some Approximation Properties of Certain q-Baskakov-Beta Operators

In this paper, we propose the q analogue of modified Baskakov-Beta opera-tors. The Voronovskaja type theorem and some direct results for the above operators are discussed. The rate of convergence and weighted approximation by the operators are studied.