On Bernstein type polynomials and their applications

Creative Commons License

ŞİMŞEK Y., GÜNAY M.

ADVANCES IN DIFFERENCE EQUATIONS, cilt.2015, ss.1-11, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2015
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1186/s13662-015-0423-9
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1-11
  • Anahtar Kelimeler: Bernstein polynomials, CAD, graphs, Bezier curves, generating functions, GENERATING-FUNCTIONS, DERIVING IDENTITIES
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.