Class Of Positive Linear Operators Research Articles

An estimate for some positive linear operators in L p spaces

In this note we prove that an estimate due to Ivanov and Pichugov, for positive linear convolution operators in Lp spaces, can be extended to a class of positive linear operators which are not of convolution type.

The iterates of positive linear operators preserving constants

In this note we introduce a simple and efficient technique for studying the asymptotic behavior of the iterates of a large class of positive linear operators preserving constant functions.

I-approximation properties of certain class of linear positive operators

In this paper we studyI-approximation properties of certain class of linear positive operators. The two main tools used in this paper areI-convergence and Ditzian-Totik modulus of smoothness. Furthermore, we defineq-Lupaş-Durrmeyer operators and give local and global approximation results for such operators.

Korovkin type approximation theorem for BBH type operators via J-convergence

Abstract This paper provides a Korovkin type approximation theorem for a class of positive linear operators including Bleimann-Butzer and Hahn operators via J-convergence.

An asymptotic formula for a class of approximation processes of King’s type

In this paper we present a general class of linear positive operators of discrete type reproducing the third test function of Korovkin theorem. In a certain weighted space it forms an approximation process. A Voronovskaja-type result is established and particular cases are analyzed.

On a generalization of Bleimann, Butzer and Hahn operators based on [formula omitted]-integers

We propose a class of linear positive operators based on q-integers. These operators depend on a non-negative parameter and represent a generalization of the classical Bleimann, Butzer and Hahn operators. Approximation properties are presented and bounds of the error of approximation are established.

Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions

We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S.N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.

On the iterates of positive linear operators preserving the affine functions

In this note we study the limit behavior of the iterates of a large class of positive linear operators preserving the affine functions and, as a byproduct of our result, we obtain the limit of the iterates of Meyer-König and Zeller operators.

On statistical approximation of a general class of positive linear operators extended in q-calculus

In this paper we present a general class of positive linear operators of discrete type based on q-calculus and we investigate their weighted statistical approximation properties by using a Bohman–Korovkin type theorem. We also mark out two particular cases of this general class of operators.

Negative Definite Cubature Formulae, Extremality and Delaunay Triangulation

Let Ω ⊂ R d be a compact convex polytope of positive measure. We study cubature formulae on Ω which approximate the integral of every convex function f ∈ C(Ω) from above. They are called negative definite formulae or nd-formulae for short. In particular, we characterize nd-formulae by certain partitions of unity or, alternatively, by a class of positive linear operators. For aiming at 'good' nd-formulae, we introduce three extremal properties named as minimal, best and optimal .W e show that the Delaunay triangulation and one of its generalizations give access to efficient algorithms for computing nd-formulae with one of these properties.

An extremal property for a class of positive linear operators

We generalize a recent result of de la Cal and Cárcamo concerning an extremal property of Bernstein operators.

Local approximation properties of certain class of linear positive operators via I—convergence

In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I—convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I—convergence sense.

About Some Linear Operators

Using the method of Jakimovski and Leviatan from their work in 1969, we construct a general class of linear positive operators. We study the convergence, the evaluation for the rate of convergence in terms of the first modulus of smoothness and we give a Voronovskaja-type theorem for these operators.

\(A\)-statistical convergence for a class of positive linear operators

In this paper we introduce a sequence of positive linear operators defined on the space \(C[0,a]\) \((0<a<1)\) and provide an approximation theorem for these operators via the concept of \(A\)-statistical convergence. We also compute the rates of convergence of these approximation operators by means of the first and second order modulus of continuity and the elements of the Lipschitz class. Furthermore, by defining the generalization of \(r\)-th order of these operators we show that the similar approximation properties are preserved on \(C[0,a].\)

On the variation detracting property of a class of operators

This work is focused upon the study of a general class of linear positive operators of discrete type. We show that, under suitable assumptions, the sequence enjoys the variation detracting property.

About a general property for a class of linear positive operators and applications

In this paper we demonstrate a general property for a class of linear positive operators. By particularization, we obtain the convergence and the evaluation for the rate of convergence in term of the first modulus of smoothness for the Bernstein operators, Durrmeyer operators, Kantorovich operators and Bleimann, Butzer and Hahn operators.

Approximation of Unbounded Functions by Linear Positive Operators

A unified class of linear positive operators has been defined. Using these operators some approximation estimates have been obtained for unbounded functions. For particular linear positive operators these results sharpen and improve the earlier estimates due to Fuhua Cheng (J. Approx. Theory, 1984) and Xiehua Sun (J. Approx. Theory, 1988).

The best asymptotic constant of a class of approximation operators

The best asymptotic constant was established by Esseen for Bernstein operators. In this paper, we extend Esseen's result to a class of linear positive operators and as byproduct we obtain the best asymptotic constant for Szász, Baskakov, Gamma, and B-Spline operators.

On the degeneracy property of some linear positive operators

The degeneracy property of a wide class of linear positive operators is investigated; a short proof of a Passow's conjecture is given for this class. Finally an application of these results in CAGD is also discussed.

A class of linear positive operators

A class of linear positive operators