Direct and inverse theorems for the Bézier variant of certain summation-integral type operators

Authors

ASHA RAM GAIROLA
P. N. AGRAWAL

DOI

10.3906/mat-0810-7

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 M_n introduced in [5] in terms of Ditzian-Totik modulus of smoothness \omega_{\varphi^\lambda}(f,t) (0 \leqslant \lambda \leqslant1 ). These operators include the well known Baskakov-Durrmeyer and Szász-Durrmeyer type operators as special cases.

Keywords

Degree of approximation, Ditzian-Totik modulus of continuity.

First Page

221

Last Page

234

Recommended Citation

GAIROLA, ASHA RAM and AGRAWAL, P. N. (2010) "Direct and inverse theorems for the Bézier variant of certain summation-integral type operators," Turkish Journal of Mathematics: Vol. 34: No. 2, Article 7. https://doi.org/10.3906/mat-0810-7
Available at: https://journals.tubitak.gov.tr/math/vol34/iss2/7