q-Bernstein polynomials and Bezier curves
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.151, sa.1, ss.1-12, 2003 (SCI-Expanded, Scopus)
- 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.