Statistical Convergence Estimates for (p, q)-Baskakov-Durrmeyer Type Operators (original) (raw)

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 the (p,q)−Stancu Generalization of a Genuine Baskakov-Durrmeyer Type Operators

2017

In this paper, we introduce a Stancu generalization of a genuine Baskakov-Durrmeyer type operators via (p,q)− integer. We investigate approximation properties of these operators. Furthermore, we study on the linear positive operators in a weighted space of functions and obtain the rate of these convergence using weighted modulus of continuity.

On Approximation of Baskakov-Durrmeyer Type Operators of Two Variables

2016

In this study, we have constructed a sequence of positive linear operators with two variables by using Baskakov-Durrmeyer type operators. We study approximation these operators and give a Voronovskaja type theorem. Furthermore , we study of the linear positive operators in a weighted space of functions of two variables and find the rate of these convergence using weighted modulus of continuity.

On Simultaneous Approximation for Certain Baskakov Durrmeyer Type Operators

Journal of Inequalities in Pure and Applied Mathematics, 2006

In the present paper, we study a certain integral modification of the well known Baskakov operators with the weight function of Beta basis function. We establish pointwise convergence, an asymptotic formula an error estimation and an inverse result in simultaneous approximation for these new operators.

On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators

International Journal of Nonlinear Analysis and Applications, 2017

In the present article, we introduce Chlodowsky variant of (p,q)(p,q)(p,q)-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function fff belongs to the class Lip$_{M}(alpha )$. Moreover, we also discuss convergence and rate of approximation in weighted spaces and weighted statistical approximation properties of the sequence of positive linear operators defined by us.

On generalized Baskakov-Durrmeyer-Stancu type operators

Demonstratio Mathematica

In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

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.

Durrmeyer variant of Apostol-Genocchi-Baskakov operators

Quaestiones Mathematicae, 2020

We study the approximation behavior of the Durrmeyer form of Apostol-Genocchi polynomials with Baskakov type operators including K-functional and second-order modulus of smoothness, Lipschitz space and find the rate of convergence for continuous functions whose derivative satisfies the condition of bounded variation. In the last section, we estimate weighted approximation behavior for these operators.

Statistical approximation properties of q-Baskakov-Kantorovich operators

Central European Journal of Mathematics, 2009

In the present paper we introduce a-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < < 1.

On statistical approximation properties of q-Baskakov–Szász–Stancu operators

Journal of the Egyptian Mathematical Society, 2016

In the present paper, we consider Stancu type generalization of Baskakov-Szász operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function are also established for operators.