Bernstein算子的强逆不等式

本文对Bernstein算子证明了其强逆不等式,这些不等式曾被Ditzian,Ivanov,Totik,李松等人用不同的方法得到过,但其结果是通常的估计(λ=1),古典的结果(λ=0)没有包含,本文引入κ-泛函K_λ~α(f,t~2)(0≤λ≤1,0<α<2),将已有结果推广到0≤λ≤1的情形。     

Szàsz-Mirakian Kantorovich算子拟中插式的逼近等价定理

本文利用高阶光滑模ω2rψ(f,t)p(1(≤)p＜∞)和ω2rψλ(f,t)∞(0(≤)λ(≤)1)得到了szàsz-Mirakian Kantorovich算子对于函数f∈Lp[0,∞)(1(≤)p(≤)∞)的逼近等价定理.     

一类修正的和与积分混合型算子的$L_p$逼近

The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces.     

W~1H_c~ω的一类宽度

本文引入函数类关于正线性算子族的线性宽度,并得到W~1H_c~ω的几种这类宽度的精确值或精确阶估计.     

Bernstein-Durrmeyer算子拟中插式的逼近

最近,为了得到更快的逼近速度,人们引入了某些著名算子的拟中插式.我们研究了Bernstein-Durrmeyer算子的拟中插式Mn(2r-1)(f,x),用Ditzian-Totik模得到了它们的正、逆定理和等价定理.这里.     

Baskakov-Durrmeyer算子的点态逼近

本文应用Ｄｉｔｚｉａｎ－Ｔｏｔｉｋ模得到Ｂａｓｋａｋｏｖ－Ｄｕｒｒｍｅｙｅｒ算子线性组合的点态逼近的等 价定理．     

ON THE RATE OF CONVERGENCE OF THE GAMMA OPERATOR FOR FUNCTIONS OF BOUNDED VARIATION

Let f be a function defined on the infinite interval[0,∞).The Gamma operator G_n applied to f isG_n(f(t),x)=∫_0~f(nt)g_n(x/t)(dt)/t,whereg_n(u)=u~ne~(-u)/(n-1)!(see[1],P.207).There are some results of convergence and saturation of G_n     

Szász-Kantorovich-Bézier算子在Lp[0,∞)上的逼近定理

本文利用Ditzian-Totik模得到了Szász-Kamorovich—Bézier算子在L_p[0,∞)空间逼近的正逆定理及等价定理．