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.     

The convergence rate of Multi-Bernstein-Durrmeyer operators with Jacobi weights

In this paper, we will consider the convergence rate of Multi-Bernstein-Durrmeyer operators with Jacobi weights and characterizations of approximation rate by means of a new K-functional.     

Asymptotic property for some series of probability

Let {X, X n , n≥1} be a sequence of i.i.d.random variables with zero mean, and set Sn = Σ k=1 n X k , EX2=σ 2>0, λ(ε) =Σ n=1 ∞ P (|Sn|≥ nε). In this paper, we discuss the rate of the approximation of σ2 by ε2 λ(ε) under suitable conditions, and improve the corresponding results of Klesov (1994).     

Simultaneous Approximation for Szsz-Mirakian-Stancu-Durrmeyer Operators

The aim of this work is to generalize Szsz-Mirakian operator in the sense of Stancu-Durrmeyer operators. We obtain approximation properties of these operators. Here we study asymptotic as well as rate of convergence results in simultaneous approximation for these modified operators.     

Some uniform convergence results for kernel estimators

This paper derives some uniform convergence rates for kernel regression of some index functions that may depend on infinite dimensional parameter. The rates of convergence are computed for independent, strongly mixing and weakly dependent data respectively. These results extend the existing literature and are useful for the derivation of large sample properties of the estimators in some semiparametric and nonparametric models.     

加权Müntz有理逼近的整体估计和点态估计

<正>1引言Müntz~([1])于1914年首先考虑了Müntz系统{x~(λn)}_(n=1)~∞在C_([0,1])中的稠密性问题,建立了著名的Müntz定理,从而将Weierstrass定理推广到了更一般的情形.对任意给定的非负递增实数序列∧={λ_n)}_(n=1)~∞,f∈C_([0,1]),令     

Complete Convergence for Weighted Sums of WOD Random Variables

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent ran-dom variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.     

A NOTE ON MEYER-KONIG AND ZELLER OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION

In the present note we give the correct and improved estimate on the rate of convergence of integratedMeyer-Konig and Zeller operators for function of bounded variation.     

Pointwise characterization for combinations of Baskakov operators

In this paper, we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totik modulus of smoothness.     

NA随机变量阵列加权和的矩完全收敛性

In this paper we obtain some new results on complete moment convergence for weighted sums of arrays of rowwise NA random variables.Our results improve and extend some well known results from the litera...     

Approximation by the Modified q-Baskakov-Sz ′asz Operators

In this paper we propose the q analogues of modified Baskakov-Sz~sz op- erators. We estimate the moments and established direct results in term of modulus of continuity. An estimate for the rate of convergence and weighted approximation properties of the q operators are also obtained.     

线性过程方差变点的平方累计和SCUSUM估计(英文)

This paper considers the estimation problem of a variance change-point in linear process.Consistency of a SCUSUM type change-point estimator is proved and its rate of convergence is established.The mean-unknown case is also considered.     

基于信赖域技术和修正拟牛顿方程的非单调共轭梯度算法

1引言考虑无约束最优化问题(?)其中f(x):R~n→R~1是一阶连续可微函数.求解问题(1)的非线性共轭梯度算法结构简单、收敛速度快、存储量小,适于求解大     

On approximation properties of non-convolution type nonlinear integral operators

In the present paper we state some approximation theorems concerning pointwise convergence and its rate for a class of non-convolution type nonlinear integral operators of the form:Tλ (f;x) = B A Kλ (t,x, f (t))dt , x ∈< a,b >, λ∈Λ. In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 of f as (x,λ ) → (x0,λ0) in L1 < A,B >, where < a,b > and < A,B > are is an arbitrary intervals in R, Λ is a non-empty set of indices with a topology and λ0 an accumulation point of Λ in this topology. The results of the present paper generalize several ones obtained previously in the papers [19]-[23].     

MNTZ RATIONAL APPROXIMATION FOR SPECIAL FUNCTION CLASSES IN Ba[0,1] SPACES

In this paper,we research the Mntz rational approximation of two kinds of special function classes,and give the corresponding estimates of approximation rates of these classes.     

Approximation by the Modified q-Baskakov-Szsz Operators

In this paper we propose the q analogues of modified Baskakov-Sz′asz operators. We estimate the moments and established direct results in term of modulus of continuity. An estimate for the rate of convergence and weighted approximation properties of the q operators are also obtained.