Approximation of Baskakov type Polya-Durrmeyer operators

作者：Gupta Vijay; Acu Ana Maria; Sofonea Daniel Florin^*

来源：Applied Mathematics and Computation, 2017, 294: 318-331.

DOI：10.1016/j.amc.2016.09.012

• Stancu operators
• Baskakov operators
• Polya-Eggenberger distribution
• Voronovskaja type theorem
• Modulus of continuity

In the present paper we propose the Durrmeyer type modification of Baskakov operators based on inverse Polya-Eggenberger distribution. First we estimate a recurrence relation by using hypergeometric series. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem. Some approximation results in weighted space are obtained. Also, we show the rate of convergence of these operators to certain functions by illustrative graphics using the Maple algorithms.

• 出版日期2017-2-1