Journals / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 2
Direct and inverse theorems for the Bézier variant of certain summation-integral type operators
- Pages
- 221–234
- DOI
- —
Abstract
Recently, the Bézier variant of some well known operators were introduced (cf. [8]-[9]) and their rates of convergence for bounded variation functions have been investigated (cf. [2], [10]). In this paper we establish direct and inverse theorems for the Bézier variant of the operators Mn introduced in [5] in terms of Ditzian-Totik modulus of smoothness wj\lambda(f,t) (0 \leqslant l \leqslant1 ). These operators include the well known Baskakov-Durrmeyer and Szász-Durrmeyer type operators as special cases.
Özet
Recently, the Bézier variant of some well known operators were introduced (cf. [8]-[9]) and their rates of convergence for bounded variation functions have been investigated (cf. [2], [10]). In this paper we establish direct and inverse theorems for the Bézier variant of the operators Mn introduced in [5] in terms of Ditzian-Totik modulus of smoothness wj\lambda(f,t) (0 \leqslant l \leqslant1 ). These operators include the well known Baskakov-Durrmeyer and Szász-Durrmeyer type operators as special cases.