Abstract

In this paper, we introduce a sequence of positive linear Beta type operators based on a function $\tau$ having certain properties. We firstly give some approximation properties of these operators. Next, we establish Voronovskaja type and Grüss-Voronovskaja type theorems in quantitative form with the help of the first order Ditzian-Totik modulus of smoothness.

Keywords: Beta operators; Voronovskaja type theorem; Grüss-Voronovskaja type theorem.

MSC: 41A36

Pages:  359--367     

Volume  71 ,  Issue  4 ,  2019