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

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 ω_φλ (f, t)(0 ≤ λ ≤ 1). These operators include the well known Baskakov-Durrmeyer and Szász-Durrmeyer type operators as special cases.