Open Access Research

Unification of the Bernstein-type polynomials and their applications

Yilmaz Simsek

Author Affiliations

Department of Mathematics, Faculty of Science, University of Akdeniz, Antalya, TR-07058, Turkey

Boundary Value Problems 2013, 2013:56  doi:10.1186/1687-2770-2013-56

Published: 20 March 2013

Abstract

In this paper, we investigate some new identities related to the unification of the Bernstein-type polynomials, Bernoulli polynomials, Euler numbers and Stirling numbers of the second kind. We also give some remarks and applications of the Bernstein-type polynomials related to solving high even-order differential equations by using the Bernstein-Galerkin method. We also give some applications on these polynomials and differential equations.

MSC: 11B68, 12D10, 14F10, 26C05, 26C10, 30B40, 30C15, 42A38, 44A10.

Keywords:
Bernstein polynomials; generating function; Bezier curves; Laplace transform; functional equation; high-order differential equations; Bernstein-Galerkin method; Bernoulli polynomials; Bernoulli numbers; Euler polynomials; Euler numbers; Genocchi polynomials; Genocchi numbers; Stirling numbers of the second kind