Some approximation results for Durrmeyer operators (original) (raw)

On the degree of approximation by new Durrmeyer type operators

General Math, 2010

In this paper, we define a new kind of positive linear operators and study basic properties as well as Voronovskaya type results. In the last section of this paper we establish the error estimation for simultaneous approximation in terms of higher order modulus of ...

On the degree of approximation by new Durrmeyer type operators 1

2010

In this paper, we deflne a new kind of positive linear operators and study basic properties as well as Voronovskaya type results. In the last section of this paper we establish the error estimation for simultaneous approximation in terms of higher order modulus of continuity by using the technique of linear approximating method viz Steklov mean. 2000 Mathematics Subject Classiflcation: 41A30, 41A36.

Improved approximation on Durrmeyer-type operators

Boletín de la Sociedad Matemática Mexicana

In the present paper, we consider the Durrmeyer-type operators, some of which reproduce the linear functions, while some the constant functions only. We observe that the order of approximation for these operators is O(n −1); here, we consider the linear combinations of such operators and study some approximation properties for these operators. Our results essentially improve the order of approximation.

Approximation properties of a certain nonlinear Durrmeyer operators

Filomat, 2017

The present paper is concerned with a certain sequence of the nonlinear Durrmeyer operators NDn, very recently introduced by the author [22] and [23], of the form (NDnf)(x)=?10 Kn (x,t,f(t))dt, 0 ? x ? 1, n ? N, acting on Lebesgue measurable functions defined on [0,1], where Kn (x,t,u) = Fn (x,t)Hn(u) satisfy some suitable assumptions. As a continuation of the very recent papers of the author [22] and [23], we estimate their pointwise convergence to functions f and ??|f| having derivatives are of bounded (Jordan) variation on the interval [0,1]. Here ?o|f| denotes the composition of the functions ? and |f|. The function ? : R0+ ? R0+ is continuous and concave with (0) = 0, ?(u) > 0 for u > 0. This study can be considered as an extension of the related results dealing with the classical Durrmeyer operators.

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.

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.

Rate of convergence of Chlodowsky type Durrmeyer Operators

In the present paper, we estimate the rate of pointwise convergence of the Chlodowsky type Durrmeyer Operators D n (f, x) for functions, defined on the interval [0, b n ], (b n → ∞), extending infinity, of bounded variation. To prove our main result, we have used some methods and techniques of probability theory.

Charlier–Szász–Durrmeyer type positive linear operators

Afrika Matematika, 2017

In the present paper, we study modified Szász-Durrmeyer positive linear operators involving Charlier polynomials, one of the discrete orthogonal polynomials which are generalization of Szász Durrmeyer operators. Also, King type modification of these operators is given. We obtain uniform convergence of our operators with the help of Korovkin theorem, asymptotic formula and the order of approximation by using classical 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 Durrmeyer-Type Variant and Generalizations of Lototsky–Bernstein Operators

Symmetry

The starting points of the paper are the classic Lototsky–Bernstein operators. We present an integral Durrmeyer-type extension and investigate some approximation properties of this new class. The evaluation of the convergence speed is performed both with moduli of smoothness and with K-functionals of the Peetre-type. In a distinct section we indicate a generalization of these operators that is useful in approximating vector functions with real values defined on the hypercube [0,1]q, q>1. The study involves achieving a parallelism between different classes of linear and positive operators, which will highlight a symmetry between these approximation processes.