Results 21 to 30 of about 189,197 (211)

Novel Formulas for B-Splines, Bernstein Basis Functions, and Special Numbers: Approach to Derivative and Functional Equations of Generating Functions

Mathematics, 2023
The purpose of this article is to give relations among the uniform B-splines, the Bernstein basis functions, and certain families of special numbers and polynomials with the aid of the generating functions method.
Yilmaz Simsek
doaj   +1 more source

Use of Bernstein Polynomial in Numerical Solution of Nonlinear Fred Holm Integral Equation [PDF]

Engineering and Technology Journal, 2011
In this paper, Bernstein polynomials with different degree has been used to approximate the solution of nonlinear Fredholm integral equations. A comparison between the different degree of Bernstein polynomials has been made depending on absolute error ...
Khawla A .AL-Zubaidy, Muna M. Mustafa
doaj   +1 more source

A New Generating Function of (q-) Bernstein-Type Polynomials and Their Interpolation Function

Abstract and Applied Analysis, 2010
The main object of this paper is to construct a new generating function of the (q-) Bernstein-type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the (q-
Yilmaz Simsek, Mehmet Acikgoz
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Some Identities of the Twisted 𝑞-Genocchi Numbers and Polynomials with Weight 𝛼 and 𝑞-Bernstein Polynomials with Weight 𝛼

Abstract and Applied Analysis, 2011
Recently mathematicians have studied some interesting relations between 𝑞-Genocchi numbers, 𝑞-Euler numbers, polynomials, Bernstein polynomials, and 𝑞-Bernstein polynomials.
H. Y. Lee, N. S. Jung, C. S. Ryoo
doaj   +1 more source

𝑞-Bernstein Polynomials Associated with 𝑞-Stirling Numbers and Carlitz's 𝑞-Bernoulli Numbers

Abstract and Applied Analysis, 2010
Recently, Kim (2011) introduced 𝑞-Bernstein polynomials which are different 𝑞-Bernstein polynomials of Phillips (1997). In this paper, we give a 𝑝-adic 𝑞-integral representation for 𝑞-Bernstein type polynomials and investigate some interesting ...
T. Kim, J. Choi, Y. H. Kim
doaj   +1 more source

Sparse polynomial interpolation with Bernstein polynomials

TURKISH JOURNAL OF MATHEMATICS, 2021
Summary: We present an algorithm for interpolating an unknown univariate polynomial \(f\) that has a \(t\) sparse representation (\(t\ll\deg(f)\)) using Bernstein polynomials as term basis from \(2t\) evaluations. Our method is based on manipulating given black box polynomial for \(f\) so that we can make use of Prony's algorithm.
openaire   +4 more sources

On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals

Discrete Dynamics in Nature and Society, 2010
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).
T. Kim, J. Choi, Y. H. Kim, L. C. Jang
doaj   +1 more source

Shape Preserving Properties for q-Bernstein-Stancu Operators

Journal of Mathematics, 2014
We investigate shape preserving for q-Bernstein-Stancu polynomials Bnq,α(f;x) introduced by Nowak in 2009. When α=0, Bnq,α(f;x) reduces to the well-known q-Bernstein polynomials introduced by Phillips in 1997; when q=1, Bnq,α(f;x) reduces to Bernstein ...
Yali Wang, Yinying Zhou
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Rate of Weighted Statistical Convergence for Generalized Blending-Type Bernstein-Kantorovich Operators

Mathematics, 2022
An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations ...
Faruk Özger, Ekrem Aljimi, Merve Temizer Ersoy   +2 more
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The Trigonometric Polynomial Like Bernstein Polynomial [PDF]

The Scientific World Journal, 2014
A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent.
openaire   +3 more sources