Bernstein-Schoenberg operator with knots at the q-integers

BUDAKÇI G., ORUÇ H.

MATHEMATICAL AND COMPUTER MODELLING, cilt.56, ss.56-59, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 56
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.mcm.2011.12.049
  • Dergi Adı: MATHEMATICAL AND COMPUTER MODELLING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.56-59
  • Anahtar Kelimeler: Bernstein-Schoenberg operator, B-spline, Marsden's identity, q-integer, POLYNOMIALS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

We consider a special knot sequence u(i+1) = qu(i) + 1 and define a one parameter family of Bernstein-Schoenberg operators. We prove that this operator converges to f uniformly for all f in C[0, 1]. This operator also inherits the geometric properties of the classical Bernstein-Schoenberg operator. Moreover we show that the error function E-m,E-n has a particular symmetry property, that is E-m,E-n(f; x; q) = E-m,E-n(f; 1 - x, 1/q) provided that f is symmetric on [0, 1]. (C) 2012 Elsevier Ltd. All rights reserved.