Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution

Abstract

In the paper the authors introduce the Kantorovich variant of Stancu operators based on Pólya-Eggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with a Voronovskaja type asymptotic formula and some estimates of the rate of approximation involving modulus of smoothness, such as Ditzian-Totik modulus of smoothness. The rate of convergence for differential functions whose derivatives are bounded is also obtained.

Keywords

• pólya-eggenberger distribution
• stancu operators
• euler functions
• rate of convergence
• 02.30.mv
• 02.30.tb