Here, we provide a unifying treatment of the convergence of a general form of sampling-type operators, given by the so-called sampling Durrmeyer-type series. The main result consists of the study of a modular convergence theorem in the general setting of Orlicz spaces (Formula presented.). From the latter theorem, the convergence in (Formula presented.), in (Formula presented.), and in the exponential spaces can be obtained as particular cases. For the completeness of the theory, we provide a pointwise and uniform convergence theorem on (Formula presented.), in case of bounded continuous and bounded uniformly continuous functions; in this context, we also furnish a quantitative estimate for the order of approximation, using the modulus of continuity of the function to be approximated. Finally, applications and examples with graphical representations are given for several sampling series with special kernels.

On the convergence properties of sampling Durrmeyer-type operators in Orlicz spaces

Costarelli D.
;
Piconi M.;Vinti G.
2023

Abstract

Here, we provide a unifying treatment of the convergence of a general form of sampling-type operators, given by the so-called sampling Durrmeyer-type series. The main result consists of the study of a modular convergence theorem in the general setting of Orlicz spaces (Formula presented.). From the latter theorem, the convergence in (Formula presented.), in (Formula presented.), and in the exponential spaces can be obtained as particular cases. For the completeness of the theory, we provide a pointwise and uniform convergence theorem on (Formula presented.), in case of bounded continuous and bounded uniformly continuous functions; in this context, we also furnish a quantitative estimate for the order of approximation, using the modulus of continuity of the function to be approximated. Finally, applications and examples with graphical representations are given for several sampling series with special kernels.
2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1553511
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