On ( p , q ) $(p,q)$ -analogue of two parametric Stancu-Beta operators

Abstract

Abstract Our purpose is to introduce a two-parametric ( p , q ) $(p, q)$ -analogue of the Stancu-Beta operators. We study approximating properties of these operators using the Korovkin approximation theorem and also study a direct theorem. We also obtain the Voronovskaya-type estimate for these operators. Furthermore, we study the weighted approximation results and pointwise estimates for these operators.

Keywords

• Stancu-Beta operators
• linear positive operators
• Lipschitz function
• modulus of continuity
• rate of convergence
• Voronovskaya-type theorem