Durrmeyer sampling-type operators: approximation in variation

Abstract In the present paper we study the approximation properties of the Durrmeyer sampling-type operators in the frame of the space of functions of bounded variation. In particular, besides some preliminary results concerning an estimate in variation of the operators in terms of the variation of the function and a regularizing property of the Durrmeyer sampling series, the main result is the convergence in variation by means of the operators. In order to prove it, a relation between the derivative of the Durrmeyer sampling series and a linear combination of the sampling Kantorovich operators applied to a convolution product involving the derivative of the function is exploited. Finally, we obtain a quantitative estimate of the rate of approximation.