On Bernstein type polynomials and their applications

Creative Commons License

ŞİMŞEK Y., GÜNAY M.

ADVANCES IN DIFFERENCE EQUATIONS, vol.2015, pp.1-11, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2015
  • Publication Date: 2015
  • Doi Number: 10.1186/s13662-015-0423-9
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-11
  • Keywords: Bernstein polynomials, CAD, graphs, Bezier curves, generating functions, GENERATING-FUNCTIONS, DERIVING IDENTITIES
  • Akdeniz University Affiliated: Yes

Abstract

In this study we examine generating functions for the Bernstein type polynomials given in (Simsek in Fixed Point Theory Appl. 2013:80, 2013). We expand these generating functions using the parameters u and v. By applying these generating functions, we obtain some functional equations and partial differential equations. In addition, using these equations, we derive several identities and relations related to these polynomials. Finally, numerical values of these polynomials for selected cases are demonstrated with their plots.

In this study we examine generating functions for the Bernstein type polynomials given in (Simsek in Fixed Point Theory Appl. 2013: 80, 2013). We expand these generating functions using the parameters u and v. By applying these generating functions, we obtain some functional equations and partial differential equations. In addition, using these equations, we derive several identities and relations related to these polynomials. Finally, numerical values of these polynomials for selected cases are demonstrated with their plots.