Work

Durrmeyer sampling-type operators: approximation in variation

Year: 2026

Type: article

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.

Source: Journal of Pseudo-Differential Operators and Applications

DOI: 10.1007/s11868-026-00764-4

Authors: Giuseppe Aiello, Laura Angeloni, Gianluca Vinti

Institutions: University of Perugia, Lucian Blaga University of Sibiu

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Perugia, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni