© Hindawi Publishing Corp. RATE OF CONVERGENCE OF BOUNDED VARIATION FUNCTIONS BY A BÉZIER-DURRMEYER VARIANT OF THE BASKAKOV OPERATORS (original) (raw)

We consider a Bézier-Durrmeyer integral variant of the Baskakov operators and study the rate of convergence for functions of bounded variation. 2000 Mathematics Subject Classification: 41A36, 41A25, 26A45. 1. Introduction. Let W(0,∞) be the class of functions f which are locally integrable on (0,∞) and are of polynomial growth as t → ∞, that is, for some positive r, there holds f(t) = O(tr) as t → ∞. The Durrmeyer variant Ṽn of the Baskakov operators associates to each function f ∈W(0,∞) the series