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

Authors

ASHA RAM GAIROLA
P. N. AGRAWAL

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.

DOI

10.3906/mat-0810-7

Keywords

Degree of approximation, Ditzian-Totik modulus of continuity.

First Page

221

Last Page

234

Recommended Citation

GAIROLA, A. R, & AGRAWAL, P. N (2010). Direct and inverse theorems for the Bézier variant of certain summation-integral type operators. Turkish Journal of Mathematics 34 (2): 221-234. https://doi.org/10.3906/mat-0810-7