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.

q−Bernstein–Schurer–Durrmeyer type operators for functions of one and two variables

Applied Mathematics and Computation, 2016

The purpose of this paper is to obtain some direct results for the Durrmeyer variant of q-Bernstein-Schurer operators for functions of one variable introduced by Acu et al. . We also propose to study the bivariate extension of these operators and discuss the rate of convergence by using the modulus of continuity, the degree of approximation for the Lipschitz class of functions and the Voronovskaja type asymptotic theorem. Furthermore, we show the convergence of the operators by illustrative graphics in Maple to certain functions in both one and two dimensional cases.

Convergence of Baskakov Durrmeyer Operators in the Reverse Order of q-Analogue

Journal of advances in mathematics and computer science, 2023

This research paper is an introduction to a new type of analogue named as-analogue for well-known Baskakov Durrmeyer operators. This new type of analogue is considered as reverse order of-analogue. In this paper, we establish the direct approximation theorem, a weighted approximation theorem followed by the estimations of the rate of convergence of these new type of operators for functions of polynomial growth on the interval .

On approximation properties of some class positive linear operators in q-analysis

Journal of Mathematical Inequalities

This paper is concerned with some sequences of the positive linear operators based on q-Calculus. The approximation properties and the rate of convergence of these sequences of q-discrete type is established by means of the modulus of continuity. Moreover we give Voronovskaya-type theorems. Finally we present some applications such as q-Bernstein operators and q-Meyer-König and Zeller operators.

Approximation properties of (p,q)-Meyer-Konig-Zeller Durrmeyer operators

Cornell University - arXiv, 2017

In this paper, we introduce Durrmeyer type modification of Meyer-König-Zeller operators based on (p, q)−integers. Rate of convergence of these operators are explored with the help of Korovkin type theorems. We establish some direct results for proposed operators. We also obtain statistical approximation properties of operators. In last section, we show rate of convergence of (p, q)−Meyer-König-Zeller Durrmeyer operators for some functions by means of Matlab programming.

Approximation by a complex q-durrmeyer type operator

ANNALI DELL'UNIVERSITA' DI FERRARA, 2012

Very recently, for 0 < q < 1 Govil and Gupta [10] introduced a certain q-Durrmeyer type operators of real variable x ∈ [0, 1] and established some approximation properties. In the present paper, for these q-Durrmeyer operators, 0 < q < 1, but of complex variable z attached to analytic functions in compact disks, we study the exact order of simultaneous approximation and a Voronovskaja kind result with quantitative estimate. In this way, we put in evidence the overconvergence phenomenon for these q-Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from the real interval [0, 1] to compact disks in the complex plane. For q = 1 the results were recently proved in Gal-Gupta [8].