q-Bernstein polynomials and Bezier curves

Oruc H., Phillips G.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.151, sa.1, ss.1-12, 2003 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 151 Sayı: 1
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1016/s0377-0427(02)00733-1
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1-12
  • Anahtar Kelimeler: generalized Bernstein polynomial, shape preserving, total positivity, degree elevation
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

We define q-Bernstein polynomials, which generalize the classical Bernstein polynomials, and show that the difference of two consecutive q-Bernstein polynomials of a function f can be expressed in terms of second-order divided differences of f. It is also shown that the approximation to a convex function by its q-Bernstein polynomials is one sided.