On the Characteristics of Difference of Some Linear Positive Operators (original) (raw)

On differences of linear positive operators

Analysis and Mathematical Physics, 2018

In this paper we consider two different general linear positive operators defined on unbounded interval and obtain estimates for the differences of these operators in quantitative form. Our estimates involve an appropriate K-functional and a weighted modulus of smoothness. Similar estimates are obtained for Chebyshev functional of these operators as well. All considerations are based on rearrangement of the remainder in Taylor's formula. The obtained results are applied for some well known linear positive operators.

Estimates for the Differences of Certain Positive Linear Operators

Mathematics, 2020

The present paper deals with estimates for differences of certain positive linear operators defined on bounded or unbounded intervals. Our approach involves Baskakov type operators, the kth order Kantorovich modification of the Baskakov operators, the discrete operators associated with Baskakov operators, Meyer-König and Zeller operators and Bleimann-Butzer-Hahn operators. Furthermore, the estimates in quantitative form of the differences of Baskakov operators and their derivatives in terms of first modulus of continuity are obtained.

A Note on the Differences of Two Positive Linear Operators

Constructive Mathematical Analysis, 2019

In the present note we find the general estimate in terms of Pǎltǎneaś modulus of continuity. In the end, we consider some examples and we apply our result for such examples to obtain the quantitative estimates for the difference of operators.

New estimates for the differences of positive linear operators

Numerical Algorithms, 2016

Using Taylor's formula some inequalities for a positive linear functional are considered in this paper. These results lead us to new estimates of the differences of certain positive linear operators. Applications for some known positive linear operators are given.

On the composition and decomposition of positive linear operators (VII)

Applicable Analysis and Discrete Mathematics, 2021

In the present paper we study the compositions of the piecewise linear interpolation operator S∆ n and the Beta-type operator Bn, namely An := S∆ n •Bn and Gn := Bn • S∆ n. Voronovskaya type theorems for the operators An and Gn are proved, substantially improving some corresponding known results. The rate of convergence for the iterates of the operators Gn and An is considered. Some estimates of the differences between An, Gn, Bn and S∆ n , respectively, are given. Also, we study the behaviour of the operators An on the subspace of C[0, 1] consisting of all polygonal functions with nodes 0, 1 2 ,. .. , n−1 n , 1. Finally, we propose to the readers a conjecture concerning the eigenvalues of the operators An and Gn. If true, this conjecture would emphasize a new and strong relationship between Gn and the classical Bernstein operator Bn.

Estimates for the differences of positive linear operators and their derivatives

Numerical Algorithms, 2019

The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Our approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of first modulus of continuity. In order to analyze the theoretical results in the last section we consider some numerical examples.

The generalized Baskakov type operators

Journal of Computational and Applied Mathematics, 2014

The use of Baskakov type operators is difficult for numerical calculation because these operators include infinite series. Do the operators expressed as a finite sum provide the approximation properties? Furthermore, are they appropriate for numerical calculation? In this paper, in connection with these questions, we define a new family of linear positive operators including finite sum by using the Baskakov type operators. We also give some numerical results in order to compare Baskakov type operators with this new defined operator.