Bézier-Summation-Integral-Type Operators That Include Pólya–Eggenberger Distribution

Abstract

We define the summation-integral-type operators involving the ideas of Pólya–Eggenberger distribution and Bézier basis functions, and study some of their basic approximation properties. In addition, by means of the Ditzian–Totik modulus of smoothness, we study a direct theorem as well as a quantitative Voronovskaja-type theorem for our newly constructed operators. Moreover, we investigate the approximation of functions with derivatives of bounded variation (DBV) of the aforesaid operators.

Keywords

• Stancu operators
• Pólya–Eggenberger distribution
• Bézier curves
• rate of convergence