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Generating functions for the Bernstein polynomials: A unified approach to deriving identities for the Bernstein basis functions
Bernstein polynomials generating function Szasz-Mirakjan basis functions
2011/2/28
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and different...
q-Bernstein polynomials associated with q-stirling numbers and Carlitz's q-Bernoulli numbers
q-Bernstein polynomial Bernoulli numbers and polynomials
2010/12/8
Recently, T. Kim([4]) introduced q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips([12]). In this paper, we give p-adic q-integral representation for Kim’s q-Bernstein po...
On p-adic analogue of q-Bernstein polynomials and related integrals
q-Bernstein polynomial Bernoulli numbers and poly-nomials p-adic q-integral
2010/12/8
Recently, T. Kim([5]) introduced q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips q-Bernstein polynomials([11, 12]). The purpose of this paper is to study some propertie...
Some identities of Bernoulli numbers and polynomials associated with Bernstein polynomials
Bernstein polynomials Bosonic p-adic integrals
2010/11/26
We investigate some interesting properties of the Bernstein poly-nomials related to the bosonic p-adic integrals on Zp.
A note on q-Bernstein polynomials
q-Bernstein polynomials q-Euler numbers q-Stirling numbers
2010/11/26
Recently, Simsek-Acikgoz([17]) and Kim-Jang-Yi([9]) have studied the q-extension of Bernstein polynomials. In this paper we propose the q-extension of Bern-stein polynomials of degree n, which are dif...
New stable numerical solutions of singular integral equations of Abel type by using normalized Bernstein polynomials
Orthonormal Bernstein polynomials Abel’s integral equations
2010/9/10
A new numerical method, based on the normalized Bernstein polynomials for solving singular integral equations of Abel type is presented here in this paper. We construct an othonormal family { }n i n i...
Use of Bernstein polynomials in numerical solutions of Volterra integral equations
Volterra integral equation Abel’s integral equation
2010/9/13
In this paper the Bernstein polynomials are used to approximate the solutions of linear Volterra integral equations. Both second and first kind integral equations, with regular, as well as weakly sing...