修正Szász算子在指数权空间的整体逼近

本文给出用修正Szász算子的逼近度刻画指数权空间中类Lip _A²α的一个特征.     

Szász-Mirakjan算子线性组合和导数的点态逼近定理

本文给出了Szász-Mirakjan算子线性组合的点态逼近定理。另外,还研究了Szász-Mirakjan算子高阶导数与所逼近函数光滑性之间的关系。     

Szász-Mirakian-Baskakov型算子的同时逼近

研究了Baskakov和Szász-Mirakian型算子的线性组合的同时逼近问题,得到了Voronovskaja型的渐进展开公式以及误差估计.     

修正的Szász算子的强逆不等式

本文证明修正的Szász算子逼近的强型正定理和逆定理,从而得到该算子逼近特征的刻画.所获结果类似于Szász算子相应的结果.     

多元Szsz—Mirkjan算子的一致逼近(英文)

本文研究了多元Szása—Mirakjan算子在C_2B(T)中的逼近性质,利用K—泛函,建立了等价的逼近定理.主要结果如下定理设f∈C_2B(T),0相似文献   

Szász型算子线性组合的同时逼近

本文利用ω^2r_φλ(f,t)代替ω^r_φλ(f,t)给出了Szász-Kantorovich算子线性组合同时逼近的估计。     

Szász型算子加权逼近的一个逆定理

利用加权光滑模ω2φλ(f,t)w研究Szász算子的点态逼近,得到Jacobi权逼近的逆定理.     

多元Szász—Mirkjan算子的一致逼近

本文研究了多元Szása—Mirakjan算子在C_2B(T)中的逼近性质,利用K—泛函,建立了等价的逼近定理.主要结果如下 定理设f∈C_2B(T),0a) ;(ii)‖S_n,m(f)-f‖_∞ =0(n^-a);(iii)a)‖f(x+tφ(x),y)-2f(x,y)+f(x-tφ(x),y)‖_∞ =0(t<     

Approximation by Szasz-Mirakjan Type Operators in L''''

M.M.Derriennic discussed the properties of Bernstein-Durrmeyer operators,M. Heilmann solved the saturation situation and the author obtained the characte-rization of their order of approximation.As extending Kantorovich polynomials inL_p[0,1]to Szász-Mirakjan-Kantorovich operators in L_p[0,∞)by V.Totik,We in-troduce a new class of Szász-Mirakjan type operators:     

Generalized Szász-Mirakjan Operator Approximation

In this paper we shall defin a kind of generahzed Szász-Mirakjan operator and discussits convergence and degree of approximation,extend some results got by J.Grof and Z.Ditzian.     

Approximation properties of Szász‐Mirakyan‐Kantorovich type operators

In this paper, we introduce and study new type Szász‐Mirakyan‐Kantorovich operators using a technique different from classical one. This allow to analyze the mentioned operators in terms of exponential test functions instead of the usual polynomial type functions. As a first result, we prove Korovkin type approximation theorems through exponential weighted convergence. The rate of convergence of the operators is obtained for exponential weights.     

Direct and strong converse theorems for a general sequence of positive linear operators

We present direct and strong converse theorems for a general sequence of positive linear operators satisfying some functional equations. The results can be applied to some extensions of Baskakov and Szász–Mirakyan operators.     

Dunkl generalization of Szász beta‐type operators

The goal in the paper is to advertise Dunkl extension of Szász beta‐type operators. We initiate approximation features via acknowledged Korovkin and weighted Korovkin theorem and obtain the convergence rate from the point of modulus of continuity, second‐order modulus of continuity, the Lipschitz class functions, Peetre's K‐functional, and modulus of weighted continuity by Dunkl generalization of Szász beta‐type operators.     

Simultaneous approximation by Szász–Mirakjan–Stancu–Durrmeyer type operators

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.     

Quantitative Estimates for Generalized Szász Operators of Max-Product Kind

We introduce a certain type generalized Szász operators of max-product kind and give an upper estimate for the error of approximation using a Shisha–Mond-type theorem.     

Asymptotic Properties of Bernstein–Durrmeyer Operators

It is known that Szász–Durrmeyer operator is the limit, in an appropriate sense, of Bernstein–Durrmeyer operators. In this paper, we adopt a new technique that comes from the representation of operator semigroups to study the approximation issue as mentioned above. We provide some new results on approximating Szász–Durrmeyer operator by Bernstein–Durrmeyer operators. Our results improve the corresponding results of Adell and De La Cal (Comput Math Appl 30:1–14, 1995).     

Some approximation results involving the q‐Szász–Mirakjan–Kantorovich type operators via Dunkl's generalization

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.     

On the Generalized Szász–Mirakyan Operators

In this paper, we construct sequences of Szász–Mirakyan operators which are based on a function ρ. This function not only characterizes the operators but also characterizes the Korovkin set ${\left \{ 1,\rho ,\rho ^{2} \right \}}$ in a weighted function space. We give theorems about convergence of these operators to the identity operator on weighted spaces which are constructed using the function ρ and which are subspaces of the space of continuous functions on ${\mathbb{R} ^{+}}$ . We give quantitative type theorems in order to obtain the degree of weighted convergence with the help of a weighted modulus of continuity constructed using the function ρ. Further, we prove some shape-preserving properties of the operators such as the ρ-convexity and the monotonicity. Our results generalize the corresponding ones for the classical Szász operators.     

(p,q)‐Generalization of Szász–Mirakyan operators

In this paper, we introduce new modifications of Szász–Mirakyan operators based on (p,q)‐integers. We first give a recurrence relation for the moments of new operators and present explicit formula for the moments and central moments up to order 4. Some approximation properties of new operators are explored: the uniform convergence over bounded and unbounded intervals is established, direct approximation properties of the operators in terms of the moduli of smoothness is obtained and Voronovskaya theorem is presented. For the particular case p = 1, the previous results for q‐Sz ász–Mirakyan operators are captured. Copyright © 2015 John Wiley & Sons, Ltd.