Bernstein-Stancu Polynomials Research Articles

On rough convergence of triple sequence spaces of Bernstein-Stancu operators of fuzzy numbers defined by a metric function

We define the concept of rough limit set of a triple sequence space of Bernstein-Stancu polynomials of fuzzy numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of Bernstein-Stancu polynomials of fuzzy numbers. Finally, we investigate some properties of the rough limit set of Bernstein-Stancu polynomials.

Korovkin-type approximation theorem for Bernstein Stancu operator of rough statistical convergence of triple sequence

We obtain a Korovkin-type approximation theorem for Bernstein Stancu polynomials of rough statistical convergence of triple sequences of positive linear operators of three variables from $H_{\omega}\left( K\right) $ to $C_{B}\left( K\right) $, where $K=[0,\infty)\times\lbrack0,\infty )\times\lbrack0,\infty)$ and $\omega$ is non-negative increasing function on $K$.

Study of Sensitivity of Parameters of Bernstein–Stancu Operators

This paper is aimed at studying sensitivity of parameters \alpha and \beta appearing in the operators introduced by D.D. Stancu [11] in 1969. Results are established on the behavior the nodes used in Bernstein-Stancu polynomials and the nodes used in Bernstein polynomials and graphical presentations of them are generated. Alternate proof of uniform convergence of Bernstein-Stancu operators and an upper bound estimation are derived. It is also established that the parameters \alpha and \beta in Bernstein-Stancu polynomials can be used to get better approximation at a point x = (\alpha)/(\beta) in [0,1] to the Bernstein polynomials.

Approximation by Durrmeyer Type Bernstein–Stancu Polynomials in Movable Compact Disks

In the present paper, we introduce a kind of complex Durrmeyer type Bernstein–Stancu polynomials in movable disks. Approximation properties by the new polynomials for analytic functions in the movable compact disks are considered.

Bernstein operator of rough I-core of triple sequences

We introduce and study some basic properties of Bernstein-Stancu polynomials of rough I-convergent of triple sequence spaces and also study the set of all Bernstein-Stancu polynomials of rough I-limits of a triple sequence spaces and relation between analytic ness and Bernstein-Stancu polynomials of rough I-core of a triple sequence spaces.

On Approximation by Bernstein–Stancu Polynomials in Movable Compact Disks

In the present paper, we introduce two kinds of complex Bernstein–Stancu polynomials and complex Kantorovich–Stancu polynomials in movable compact disks. Their approximation properties for analytic functions in the movable compact disks are considered.

On the Convergence of Bernstein-Stancu Polynomials in the Variation Seminorm

ABSTRACTThis article studies the variation detracting property and rate of approximation of the Bernstein-Stancu polynomials in the space of functions of bounded variation with respect to the variation seminorm. Moreover, we will present Voronovskaya-type theorems for Bernstein-Stancu polynomials Bn, α, βf and for the first derivative of these polynomials. Finally we include some graphical examples.

On the approximation by operators of Bernstein–Stancu types

Recently, Gadjiev and Ghorbanalizadeh (2010) introduced a new type of generalized Bernstein–Stancu polynomials, and obtained a direct result (see Gadjiev and Ghorbanalizadeh, 2010, Theorem 2). In the present paper, we obtain both the direct result and the inverse result of approximation by the polynomials. Our results are pointwise. Furthermore, we also consider the approximation by a type of more generalized Bernstein–Stancu operators introduced by Taşdelen et al. (2012) for functions of smoothness.

Shape Preserving Properties forq-Bernstein-Stancu Operators

We investigate shape preserving forq-Bernstein-Stancu polynomialsBnq,α(f;x)introduced by Nowak in 2009. Whenα=0,Bnq,α(f;x)reduces to the well-knownq-Bernstein polynomials introduced by Phillips in 1997; whenq=1,Bnq,α(f;x)reduces to Bernstein-Stancu polynomials introduced by Stancu in 1968; whenq=1,α=0, we obtain classical Bernstein polynomials. We prove that basicBnq,α(f;x)basis is a normalized totally positive basis on[0,1]andq-Bernstein-Stancu operators are variation-diminishing, monotonicity preserving and convexity preserving on[0,1].

Approximation properties of a new type Bernstein–Stancu polynomials of one and two variables

A new generalization of Bernstein–Stancu type polynomials for one and two variables are constructed and the theorems on convergence and the degree of convergence are established. In addition some numerical examples, corresponding to obtaining results are given.

Approximation by Complex Bernstein–Stancu Polynomials in Compact Disks

In this paper, the order of simultaneous approximation, a Voronovskaja kind result with quantitative estimate and convergence results of the iterates, for complex Bernstein–Stancu polynomials (depending on two parameters) attached to analytic functions on compact disks are obtained.

Exact orders in simultaneous approximation by complex Bernstein-Stancu polynomials

In this paper the exact orders in approximation by the complex Bernstein-Stancu polynomials (depending on two parameters) and their derivatives on compact disks are obtained.

Approximation and geometric properties of some complex Bernstein-Stancu polynomials in compact disks

In this paper, the order of simultaneous approximation, convergence results of the iterates and shape preserving properties, for complex Bernstein-Stancu polynomials (depending on one parameter) attached to analytic functions on compact disks are obtained.