<Emphasis Type="Italic">L</Emphasis><Superscript>p</Superscript> approximation by general Bernstein-Durrmeyer operator defined on simplex

As a generalization of the Bernstein-Durrmeyer operators defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decomposition way. From the theorems the characterization of L^p approximation behavior is derived     

一类推广的Bernstein-Kantorovich算子的点态逼近

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.     

Bernstein-Sikkema-Bézier算子的点态逼近

讨论了Bernstein-Sikkema-Bézier算子点态逼近的等价定理,首先利用插项的的方法证明了正定理,然后应用讨论算子逼近的常规方法给出了其逼近的逆定理.     

Bernstein-Kantorovich 算子线性组合同时逼近的正逆定理

借助光滑模ωtφ三(f,t)给出了Bernstein-Kantorovich 算子线性组合同时逼近的正逆定理,其中φ是一般步权函数,对已有的结果进行了补充和完善.     

Baskakov型算子同时逼近的点态估计

In this paper, for Baskakov, Baskakov-Kantorovich and Baskakov-Durrmyer operators Ln(f,x),we give a simultaneous approximation of equivalent theorem with ω^2ψλ (f, t) The theorem unites the corrosponding results of classical and the Ditzian-Totik moduli of smoothness.     

THE GLOBAL APPROXIMATION BY LEFT-BERNSTEIN-DURRMEYER QUASI-INTERPOLANTS IN Lp[0,1]

In this paper, we will use the 2r-th Ditzian-Totik modulus of smoothness wψ2r(f,t)p to discuss the direct and inverse theorem of approximation by Left-Bernstein-Durrmeyer quasi-interpolants Mn[2r-1]f for functions of the space Lp[0,1] (1≤ p≤ +∞).     

Bernstein 算子的同时逼近

借助于D itzian-T otik光滑模研究了Bernstein算子的同时逼近问题,给出了Bernstein算子同时逼近的正定理和等价定理.     

球面卷积算子逼近

研究d维欧氏空间R~d中单位球面上卷积算子的逼近问题.利用球面乘子理论以及K-泛函与光滑模等价关系,建立一类球面卷积算子逼近的正、逆定理.特别地,给出了逼近的强型逆向不等式,从而揭示了该类球面卷积算子的本质逼近阶.此外,作为应用,给出了球面Jackson-Matsuoka卷积算子与Abel-Poisson卷积算子逼近上、下界的相同阶估计.     

Equivalent theorems on simultaneous approximation by combinations of Gamma operators

In this paper,some equivalent theorems on simultaneous approximation for combinations of Gamma operators by weighted moduli of smoothness ωr(4)λ(f,t)w(4)s(O≤λ≤1)are given.The relation between derivatives of combinations of Gamma operators and smoothness of derivatives of functions is also investigated.     

Bernstein型算子加Jacobi权逼近

对于Bernstein型算子,证明它在通常的加权范数下是无界的,通过引进新的加权范数,研究其加Jacobi权的逼近性质,得到加权逼近的正逆定理,从而导出加权逼近特征的等价刻画．     

多元Bernstein-Durrmeyer型多项式及其逼近特征

作为Bernstein-Durrmeyer多项式的推广,定义单纯形上的Bernstein-Durrmeyer型多项式.以最佳多项式逼近为度量,给出Bernstein-Durrmeyer型多项式Lp逼近阶的估计,并且以一个逆向不等式的形式建立其Lp逼近的逆定理,从而用最佳多项式逼近刻画该多项式Lp逼近的特征.所获结果包含了多元Bernstein-Durrmeyer多项式的相应结果.     

THE GLOBAL APPROXIMATION BY LEFT-BERNSTEIN-DURRMEYER QUASI-INTERPOLANTS IN Lp[0, 1]

In this paper,we will use the 2r-th Ditzian-Totik modulus of smoothness wp^2r(f,t)p to discuss the direct and inverse theorem of approximation by Left-Bernstein-Durrmeyer quasi-interpolants Mn^[2r-1]f for functions of the space Lp[0,1](1≤p≤ ∞)。     

Pointwise Estimate for Linear Combinations of Bernstein-Kantorovich Operators

For linear combinations of Bernstein-Kantorovich operators K_n, r(f, x), we give an equivalent theorem with ω^2r_?^λ(f, t). The theorem unites the corresponding results of classical and Ditzian-Totik moduli of smoothness.     

Bernstein-Sikkema算子逼近

研究Ｂｅｒｎｓｔｅｉｎ－Ｓｉｋｋｅｍａ算子的逼近问题,得到强型正定理和弱型逆定理,改进了文献［１］的结果     

Orlicz空间中的多元光滑模及其应用

本文的目的是引进和应用Orlicz空间中一种新的多元光滑模，该光滑模是一元情形的一种自然推广．利用函数分解方法和归纳讨论证明它与K-泛函之间的等价关系．作为应用，给出定义在单纯形上Durrmeyer算子在Orlicz空间中的一个逼近逆定理．     

Meyer-KnigandZeller算子的保形问题

讨论了 Meyer-Knig and Zeller算子的保形逼近问题 ,我们用基于算子特殊结构的分析方法得到了该算子的保单调性 .保凸性以及保形逆定理等保形性质 .     

Sz\''asz-Kantorovich-B\''{e}zier算子在$L_p[0, \infty)$上的逼近定理

本文利用Ditzian-Totik模得到了Sz\'{a}sz-Kantorovich-B\'{e}zier算子在$L_{p}[0,\infty)$空间逼近的正逆定理及等价定理.     

Rank theorems of operators between Banach spaces

Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.     

Lp空间Shepard算子逼近的正逆定理

本文引入了一种修正的积分型Shepard算子,建立了相应的Jackson型定理,并通过建立Bernstein型不等式,给出了算子在L[0,1]p空间中一种新的逼近阶刻画的等价形式,得到了逼近的逆定理．