APPROXIMATION BY COMPLEX SZSZ-DURRMEYER OPERATORS IN COMPACT DISKS

In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.

Approximation by Complex Baskakov-Szsz-Durrmeyer Operators in Compact Disks

In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; ｜z｜ 〈 R}. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on [0,∞）.

L^p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_(0,0) ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 （= F 0 , 2 1 ） → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p （= F 0 , 2 p ） → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.

Approximation by the Modified q-Baskakov-Szsz 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.

Approximation properties for the genuine modi ed Bernstein-Durrmeyer-Stancu operators

In this paper,we study on the genuine modified Bernstein-Durrmeyer-Stancu operators Gn(f,x)and investigate some approximation properties of them.Furthermore,we present a Voronovskaja type theorem for these operators.We also give some graphs and numerical examples to illustrate the convergence properties of these operators for certain functions.

A Note on the Statistical Approximation Properties of the Modified Discrete Operators

In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of continuity of these positive linear operators. Finally, we obtain the rate of statistical convergence of truncated operators.

ON CONSERVATIVE APPROXIMATION BY LINEAR POLYNOMIAL OPERATORS AN EXTENSION OF THE BERNSTEIN'S OPERATOR

In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.

Expansions and Improvements for Functions Approximation Based on F-operator

通过在这篇论文的 F 操作员的问题上的进一步的学习， f (x) 的一些研究结果由 F 接近了(f， x ) 被扩大，一些精确被精制；同时，常数进一步被改进。

Pointwise Estimate for Baskakov Operators

There are some equivalence theorems on Baskakov Operators. In this paper, we make use of ω 2 φ λ (f;t) to give a new equivalence theorem which includes the existing results as its special cases.

Consequence Operators and Information Algebras

In this paper, the continuity of consequence operators is introduced. Relations between consequence operators and their associated information algebras are mainly explored. It is shown that, for any given consequence operator, the associated information algebra can be directly constructed without any additional conditions.Furthermore, if the consequence operators are continous or compact, then the associated information algebras are continuous or compact.

BROWDER AND SEMI-BROWDER OPERATORS

In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of closed densely defined linear operators on Banach spaces.

Converse Result on Szász-Type Operators

Szász-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szász-type operators by Steckin-Marchaud-type inequalities and new Ditzian modulus of continuity. The degree of approximation on deterministic signals is also given.

Quantitative Characterizations of Bounded Compact Approximation Property by Semi-Fredholm Operators

Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.

On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions

By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.

On Approximation of Nonbounded Continuous Functions

This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.

The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators

This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.

Stochastic Approximation Method for Fixed Point Problems

We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.

An approximation problem of the finite rank operator in Banach spaces

By the method of geometry of Banach spaces, we have proven that a bounded linear operatorin Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rankbounded homogeneous operators, which reveals the essence of the counter example given by Enflo.

Approximation by q Baskakov Beta Operators

In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obtain point-wise estimate, using the Lipschitz type maximal function.

Strong Convergence Theorems of Viscosity Approximation for Accretive Operators

Let E be a real Banach space and let A be an m-accretive operator with a zero. Define a sequence {x_n} as follows:x_n+1=α_nf(x_n)+(1-α_n)J_r_n x_n,where {α_n},{r_n} are sequences satisfying certain conditions,and J_r denotes the resolvent(I+rA)^(-1)for r>1.Strong convergence of the algorithm {x_n} is obtained provided that E either has a weakly continuous duality map or is uniformly smooth.