Blending Type Approximation Research Articles

Bivariate Lupaş-Durrmeyer type operators involving Pólya distribution

In this paper, we consider a bivariate extension of blending type approximation by Lupa?-Durrmeyer type operators involving P?lya Distribution. We illustrate the convergence rate of these type operators using Peetre?s K-functional, modulus of smoothness and for functions in a Lipschitz type space.

Blending type approximation by modified Bernstein operators

Blending type approximation by modified Bernstein operators

Blending type approximation by bivariate generalized Bernstein type operators

In this article we establish an extension of the bivariate generalization of the Bernstein type operators involving parameters. For these operators we obtain a Voronovskaja type and Grüss Voronovskaja type theorems and the degree of approximation by means of the Lipschitz type space. Further, we present the associated Generalized Boolean Sum (GBS) operators and establish their degree of approximation in terms of the mixed modulus of smoothness. The comparison of convergence of the bivariate Bernstein type operators based on parameters and its GBS type operators is shown by illustrative graphics using MAPLE software.

Blending type approximation by GBS operators of bivariate tensor product of \u03bb-Bernstein\u2013Kantorovich type

In this paper, we introduce a family of GBS operators of bivariate tensor product of λ-Bernstein–Kantorovich type. We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaja type asymptotic formula for the bivariate λ-Bernstein–Kantorovich operators, as well as give some examples and their graphs to show the effect of convergence.

Blending type approximation by Stancu-Kantorovich operators associated with the inverse Pólya-Eggenberger distribution

In this paper, we give some approximation properties by Stancu-Kantorovich operators based on inverse Pólya-Eggenberger distribution in the polynomial weighted space introduced in the literature and obtain convergence properties of these operators by using Korovkin's theorem. We discuss the direct result and Voronovskaja type asymptotic formula.

Blending-type approximation by generalized Lupaş–Durrmeyer-type operators

In this note, we present a Durrmeyer-type modification of generalized Lupas operators depending on certain parameter $$\rho >0$$ . We establish quantitative asymptotic result, some direct results, weighted approximation and the order of convergence for the functions having a derivative equivalent with a function of bounded variation for these operators.

Blending Type Approximation by GBS Operators of Generalized Bernstein–Durrmeyer Type

In this article we study an extension of the bivariate generalized Bernstein–Durrmeyer operators based on a non-negative real parameter. For these operators we get a Voronovskaja type theorem, the order of approximation using Peetre’s K-functional and the degree of approximation by means of the Lipschitz class. Further, we introduce the generalized boolean sum operators of generalized Bernstein–Durrmeyer type and we estimate the degree of approximation in terms of the mixed modulus of smoothness.

Blending type approximation by bézier-summation-integral type operators

In this note we construct the B€zier variant of summation integral type operators based on a non-negative real parameter. We present a direct approximation theorem by means of the first order modulus of smoothness and the rate of convergence for absolutely continuous functions having a derivative equivalent to a function of bounded variation. In the last section, we study the quantitative Voronovska ja type theorem

Blending type approximation by generalized Bernstein-Durrmeyer type operators

Blending type approximation by generalized Bernstein-Durrmeyer type operators

Blending type approximation by generalized Szász type operators based on Charlier polynomials

In the present paper, we introduce a generalized Szasz type operators based on ´ ρ(x) where ρ is a continuously differentiable function on [0, ∞), ρ(0) = 0 and inf ρ 0 (x) ≥ 1, x ∈ [0, ∞). This function not only characterizes the operators but also characterizes the Korovkin set 1, ρ, ρ2 in a weighted function space. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain a Voronovskaja type result and the rate of convergence in terms of the weighted modulus of continuity.

Blending-type approximation by generalized Lupaş-type operators

In this note, we introduce generalization of Lupas operators which reproduce constant functions. We study quantitative asymptotic result, some local-direct results and the rate of convergence for the functions having a derivative equivalent with a function of bounded variation for these operators. Furthermore, we illustrate the convergence of the operators with the help of Mathematica software.

Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution

Abstract In the paper the authors introduce the Kantorovich variant of Stancu operators based on Pólya-Eggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with a Voronovskaja type asymptotic formula and some estimates of the rate of approximation involving modulus of smoothness, such as Ditzian-Totik modulus of smoothness. The rate of convergence for differential functions whose derivatives are bounded is also obtained.

Blending Type Approximation by Bivariate BernsteinKantorovich operators

Blending Type Approximation by Bivariate BernsteinKantorovich operators

Blending type approximation by q‐generalized Boolean sum of Durrmeyer type

This paper is in continuation of the work performed by Kajla et al. (Applied Mathematics and Computation 2016; 275 : 372–385.) wherein the authors introduced a bivariate extension of q‐Bernstein–Schurer–Durrmeyer operators and studied the rate of convergence with the aid of the Lipschitz class function and the modulus of continuity. Here, we estimate the rate of convergence of these operators by means of Peetre's K‐functional. Then, the associated generalized Boolean sum operator of the q‐Bernstein–Schurer–Durrmeyer type is defined and discussed. The smoothness properties of these operators are improved with the help of mixed K‐functional. Furthermore, we show the convergence of the bivariate Durrmeyer‐type operators and the associated generalized Boolean sum operators to certain functions by illustrative graphics using Maple algorithm. Copyright © 2017 John Wiley & Sons, Ltd.