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Approximation by the Bézier variant of the MKZ-Kantorovich operators in the case α < 1

Xiao-Ming Zeng, Vijay Gupta (2009)

Open Mathematics

The pointwise approximation properties of the Bézier variant of the MKZ-Kantorovich operators M ^ n , α ( f , x ) for α ≥ 1 have been studied in [Comput. Math. Appl., 39 (2000), 1-13]. The aim of this paper is to deal with the pointwise approximation of the operators M ^ n , α ( f , x ) for the other case 0 < α < 1. By means of some new techniques and new inequalities we establish an estimate formula on the rate of convergence of the operators M ^ n , α ( f , x ) for the case 0 < α < 1. In the end we propose the q-analogue of MKZK operators....

Approximation properties for modified ( p , q ) -Bernstein-Durrmeyer operators

Mohammad Mursaleen, Ahmed A. H. Alabied (2018)

Mathematica Bohemica

We introduce modified ( p , q ) -Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators D n , p , q * and compute the rate of convergence for the function f belonging to the class Lip M ( γ ) .

Approximation properties of q-Baskakov operators

Zoltán Finta, Vijay Gupta (2010)

Open Mathematics

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.

Bernstein type operators having 1 and x j as fixed points

Zoltán Finta (2013)

Open Mathematics

For certain generalized Bernstein operators {L n} we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions e i(x) = x i and e j (x) = x j are preserved by L n for each n = 1, 2,… But there exist infinitely many e i such that e 0(x) = 1 and e j (x) = x j are its fixed points.

Bernstein-type operators on the half line

Antonio Attalienti, Michele Campiti (2002)

Czechoslovak Mathematical Journal

We define Bernstein-type operators on the half line [ 0 , + ∞ [ by means of two sequences of strictly positive real numbers. After studying their approximation properties, we also establish a Voronovskaja-type result with respect to a suitable weighted norm.

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