Some approximation properties of q-Durrmeyer- Schurer operators (original) (raw)

Some approximation properties of a Durrmeyer variant ofq-Bernstein-Schurer operators

Mathematical Methods in the Applied Sciences, 2016

Our goal is to present approximation theorems for a Durrmeyer variant of q-Bernstein-Schurer operators define by C.V. Muraru and modified by M.Y. Ren and X.M. Zeng. C.V. Muraru and A.M. Acu studied the Durrmeyer variant of the original q-Bernstein-Schurer using uniforme convergence. Our choice is to use both, the uniforme convergence and the statistical convergence to establish some approximation theorems for the Durrmeyer variant of the modified q-Bernstein-Schurer operators.

A note on approximation properties of q-Durrmeyer operators

In this paper, the approximation properties of q-Durrmeyer operators D n;q ðf ; xÞ for f 2 C½0; 1 are discussed. The exact class of continuous functions satisfying approximation process lim n!1 D n;q ðf ; xÞ ¼ f ðxÞ is determined. The results of the paper provide an elaboration of the previously-known ones on operators D n;q .

On approximation to discrete q-derivatives of functions via q-Bernstein-Schurer operators

Mathematical Foundations of Computing, 2021

In the present paper, we shall investigate the pointwise approximation properties of the q−analogue of the Bernstein-Schurer operators and estimate the rate of pointwise convergence of these operators to the functions f whose q−derivatives are bounded variation on the interval [0, 1 + p]. We give an estimate for the rate of convergence of the operator (Bn,p,qf) at those points x at which the one sided q−derivatives D + q f (x) and D − q f (x) exist. We shall also prove that the operators (Bn,p,qf) (x) converge to the limit f (x). As a continuation of the very recent and initial study of the author deals with the pointwise approximation of the q−Bernstein Durrmeyer operators [12] at those points x at which the one sided q−derivatives D + q f (x) and D − q f (x) exist, this study provides (or presents) a forward work on the approximation of q-analogue of the Schurer type operators in the space of DqBV .

Some approximation properties of q-Durrmeyer operators

Applied Mathematics and Computation, 2008

In the present paper, we introduce a simple q analogue of well known Durrmeyer operators. We first estimate moments of q-Durrmeyer operators. We also establish the rate of convergence for q-Durrmeyer operators.

On Approximation Properties of Generalized q-Bernstein Operators

Numerical Functional Analysis and Optimization

In this study, a (p, q)-analogue of Bernstein operators is introduced and approximation properties of (p, q)-Bernstein operators are investigated. Some basic theorems are proved. The rate of approximation by modulus of continuity is estimated.

Certain Generalized q-Operators

Demonstratio Mathematica, 2015

The applications of q-calculus in the approximation theory is a very interesting area of research in the recent years, several new q-operators were introduced and their behaviour were discussed by many researchers. This paper is the extension of the paper [15], in which Durrmeyer type generalization of q-Baskakov-Stancu type operators were discussed by using the concept of q-integral operators. Here, we propose to study the Stancu variant of q-Baskakov-Stancu type operators. We establish an estimate for the rate of convergence in terms of modulus of continuity and weighted approximation properties of these operators.

On discrete q-derivatives of q-Bernstein operators

Bulletin of the "Transilvania" University of Braşov, 2022

In the present paper we shall investigate the pointwise approximation properties of the q analogue of the Bernstein operators and estimate the rate of pointwise convergence of these operators to the functions f whose qderivatives are bounded variation on the interval [0, 1]. We give an estimate for the rate of convergence of the operator (B n,q f) at those points x at which the one sided q-derivatives D + q f (x), D − q f (x) exist. We shall also prove that the operators B n,q f converge to the limit f. As a continuation of the very recent study of the author on the q-Bernstein Durrmeyer operators [10], the present study will be the first study on the approximation of q analogous of the discrete type operators in the space of D q BV .