Recently, Kim’s work in press introduced q-Bernstein polynomials which are different Phillips’ q-Bernstein polynomials introduced in the work by Phillips, 1996; 1997 . The purpose of this paper is to study some properties of several type Kim’s q-Bernstein polynomials to express the p-adic q-integral of these polynomials on Zp associated with Carlitz’s q-Bernoulli numbers and polynomials. Finall...

This paper is aimed at studying sensitivity of parameters α and β 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 ...

A new formula expressing explicitly the derivatives of Bernstein polynomials of any degree and for any order in terms of Bernstein polynomials themselves is proved, and a formula expressing the Bernstein coefficients of the general-order derivative of a differentiable function in terms of its Bernstein coefficients is deduced. An application of how to use Bernstein polynomials for solving high ...

In paper [4], transformation matrices mapping the Legendre and Bernstein forms of a polynomial of degree n into each other are derived and examined. In this paper, we derive a matrix of transformation of Chebyshev polynomials of the first kind into Bernstein polynomials and vice versa. We also study the stability of these linear maps and show that the Chebyshev–Bernstein basis conversion is rem...

We define the notion of Bernstein measures and Bernstein approximations over general convex polytopes. This generalizes well-known Bernstein polynomials which are used to prove the Weierstrass approximation theorem on one dimensional intervals. We discuss some properties of Bernstein measures and approximations, and prove an asymptotic expansion of the Bernstein approximations for smooth functi...

We begin by classifying all solutions of two natural recurrences that Bernstein polynomials satisfy. The first scheme gives a natural characterization of Stancu polynomials. In Section 2, we identify the Bernstein polynomials as coefficients in the generating function for the elementary symmetric functions, which gives a new proof of total positivity for Bernstein polynomials, by identifying th...

Global and local Bernstein-Sato ideals, Bernstein-Sato polynomials and Bernstein-Sato polynomials of varieties are introduced, their basic properties are proven and their algorithmic determination with the method of Briançon/Maisonobe is presented. Strati cations with respect to the local variants of the introduced polynomials and ideals with the methods of Bahloul/Oaku and Levandovskyy/Martín-...

in this paper, the ritz-galerkin method in bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (mhd) flow of third grade fluid between the two plates. the properties of the bernstein  polynomials together with the ritz-galerkin method are used to reduce the solution of the mhd couette flow of non-newtonian fluid in a porous medium to the solution o...

We present approximation kernels for orthogonal expansions with respect to Bernstein-Szegö polynomials. The construction is derived from known results for Chebyshev polynomials of the first kind and does not pose any restrictions on the Bernstein-Szegö polynomials.