一类修正的Durrmeyer型q-Baskakov算子的统计收敛性质

本文基于q-积分的概念,定义了一类新的修正的Durrmeyer型q-Baskakov算子,应该指出该算子不同于Aral和Gupta(2010)所定义的算子.通过计算得到算子的各阶矩量及中心矩,研究了算子的统计收敛性质并得到Voronovskaya型渐近展开公式.     

Durrmeyer type modification of generalized Baskakov operators

In the present paper, Durrmeyer type modification of generalized Baskakov operators is introduced and some direct results are established for these operators.     

q-Baskakov型算子的A-统计逼近

引入一类q-Baskakov型算子,对一个非负正则可求和矩阵A,应用A-统计逼近的理论,研究了这类修正的Korovkin型统计逼近性质.对于0q≤1,借助连续性模,证得这类q-Baskakov型算子的收敛速度要优于q-Baskakov算子.     

On simultaneous approximation of the Bernstein Durrmeyer operators

The present paper deals with the study of the rate of convergence of the Bézier variant of certain Bernstein Durrmeyer type operators in simultaneous approximation.     

Approximation properties of q-Baskakov operators

We establish direct estimates for the q-Baskakov operator introduced by Aral and Gupta in [2], using the second order Ditzian-Totik modulus of smoothness. Furthermore, we define and study the limit q-Baskakov operator.     

Approximation by Durrmeyer type Jakimoski–Leviatan operators

In this study, we introduce the Durrmeyer type Jakimoski–Leviatan operators and examine their approximation properties. We study the local approximation properties of these operators. Further, we investigate the convergence of these operators in a weighted space of functions and obtain the approximation properties. Furthermore, we give a Voronovskaja type theorem for the our new operators. Copyright © 2015 John Wiley & Sons, Ltd.     

Some approximation results for Durrmeyer operators

In the present paper, we obtain a sequence of positive linear operators which has a better rate of convergence than the Szász-Mirakian Durrmeyer and Baskakov Durrmeyer operators and their Voronovskaya type results.     

On certain Durrmeyer type <Emphasis Type=Italic>q</Emphasis> Baskakov operators

In this paper we introduce the q analogue of certain Durrmeyer type Baskakov operators. These operators were first considered by Finta (J Math Anal Appl 312:159–180, 2005). We establish direct results in terms of modulus of continuity.     

Uniform approximation by some Durrmeyer operators

The purpose of this paper is to give the inverse theorems for uniform approximation by Bernstein and Szász-Mirakjan Durrmeyer operators. A new K-functional is introduced which shows the instinct difference between Feller and non-Feller operators. A new approach to the inverse theorem for Bernstein operators is also presented. Supported by National Science Foundation of China     

King type modification of q-Bernstein-Schurer operators

Very recently the q-Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve x ² (2003), in this paper we modify q-Bernstein-Schurer operators to King type modification of q-Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions x ² and study the approximation properties of these operators. We establish a convergence theorem of Korovkin type. We also get some estimations for the rate of convergence of these operators by using modulus of continuity. Furthermore, we give a Voronovskaja-type asymptotic formula for these operators.     

Statistical approximation properties of the Durrmeyer type q‐Bleimann,Butzer, and Hahn operators

In this paper, we introduce a Durrmeyer‐type generalization of q‐Bleimann, Butzer, and Hahn operators based on q‐integers and obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. We also compute rates of statistical convergence of these q‐type operators by means of the modulus of continuity and Lipschitz‐type maximal function, respectively. Copyright © 2011 John Wiley & Sons, Ltd.     

关于任意三角形区域上的Durrmeyer算子

本文将区间[0,1]上的Durrmeyer算子推广到平面上的任意三角形区域中去,并在空间C(T),C^k(T)(k≥1),L_p(T)以及Sobolev空间W_pr(T)中研究了它的收敛性及逼近度估计,这里T是平面上的三角形区域。     

Asymptotic formulas for generalized Baskakov‐Durrmeyer operators

The paper deals with general Baskakov‐Durrmeyer operators containing several previous definitions as special cases. We construct a new sequence of BaskakovDurrmeyer operators depending on a parameter γ. We present a quantitative Voronovskaya type theorem in terms of weighted modulus of smoothness using sixth‐order central moment. In addition, we studied Grü ss‐type Voronovskaya theorem. All results in this work show that our new operators are flexible and sensitive to the rate of convergence to f, depending on our selection of γ(x).     

On the Durrmeyer-type modification of some discrete approximation operators

In [10], for continuous functionsf from the domain of certain discrete operatorsL _n the inequalities are proved concerning the modulus of continuity ofL _nf. Here we present analogues of the results obtained for the Durrmeyer-type modification $\tilde L_n $ ofL _n. Moreover, we give the estimates of the rate of convergence of $\tilde L_n f$ in Hölder-type norms     

On the integrated Baskakov type operators

The present paper deals with the study of the rate of convergence of the integrated Baskakov-Durrmeyer type operators in simultaneous approximation. We also mention some of the improvements on the recent paper of Deo [N. Deo, Direct results on exponential type operators, Applied Mathematics and Computation 204(1) (2008) 109-115].     

Studying Baskakov–Durrmeyer operators and quasi-interpolants via special functions

We prove that the kernels of the Baskakov–Durrmeyer and the Szász–Mirakjan–Durrmeyer operators are completely monotonic functions. We establish a Bernstein type inequality for these operators and apply the results to the quasi-interpolants recently introduced by Abel. For the Baskakov–Durrmeyer quasi-interpolants, we give a representation as linear combinations of the original Baskakov–Durrmeyer operators and prove an estimate of Jackson–Favard type and a direct theorem in terms of an appropriate K-functional.     

On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

On the norms of generalized translation operators generated by Dunkl type operators

An integral representation for the generalized translation operators generated by Dunkl type operators $$ \Lambda f(x) = f'(x) + \frac{{A'(x)}}{{A(x)}}\frac{{f(x) - f\left( { - x} \right)}}{2} $$ In the spaces $ {L_p}\left( \mathbb{R} \right) $ with weight A is established, and a known estimate for their norms is improved. It is proved that under some natural assumptions on the functions A, these norms do not exceed two. Bibliography: 24 titles.     

On convergence of general Gamma type operators

The present paper deals with the new type of Gamma operators, here we esti- mate the rate of pointwise convergence of these new Gamma type operators Mn,k for func- tions of bounded variation, by using some techniques of probability theory.