Rate of convergence of the Bezier variant of an operator involving Laguerre polynomials

Oksuzer O., KARSLI H., TAŞDELEN YEŞİLDAL F.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.41, sa.3, ss.912-919, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1002/mma.3705
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.912-919
  • Anahtar Kelimeler: rate of convergence, Laguerre polynomials, Bezier basis, Chanturia's modulus of variation, SERIES
  • Ankara Üniversitesi Adresli: Evet

Özet

In the present paper, we consider the Bezier variant of an operator involving Laguerre polynomials of degree k,with 1, for bounded functions f defined on the interval [0,1]. In particular, by using the Chanturia modulus of variation, we estimate the rate of pointwise convergence of (P(n,)f)(x,t) at those points x(0,1) at which the one-sided limits f(x+),f(x-) exist. To prove our main result, we have used some methods and techniques of probability theory. Our result extends and generalizes the very recent results of very recent results of the authors to more general classes of functions. Copyright (c) 2016 John Wiley & Sons, Ltd.