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.

Keywords: Degree of approximation, Ditzian-Totik modulus of continuity.

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