On generalized Baskakov-Durrmeyer-Stancu type operators

Abstract

In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

Keywords

• Baskakov-Durrmeyer-Stancu operators
• Lipschitz type space
• rate of convergence
• modulus of smoothness
• A-statistical convergence
• 26A15
• 26A16
• 41A25
• 41A36