Unification of the Bernstein-type polynomials and their applications

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Simsek Y.

BOUNDARY VALUE PROBLEMS, vol.2013, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-2770-2013-56
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • 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, GENERATING-FUNCTIONS, BERNOULLI, EULER
  • Akdeniz University Affiliated: Yes


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.