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Approximation by sampling Kantorovich series in weighted spaces of functions
(Tubitak Scientific & Technological Research Council Turkey, 2022) Acar, Tuncer; Alagöz, Osman; Aral, Ali; Costarelli, Danilo; Turgay, Metin; Vinti, Gianluca
This paper studies the convergence of the so-called sampling Kantorovich operators for functions belonging to weighted spaces of continuous functions. This setting allows us to establish uniform convergence results for functions that are not necessarily uniformly continuous and bounded on R. In that context we also prove quantitative estimates for the rate of convergence of the family of the above operators in terms of weighted modulus of continuity. Finally, pointwise convergence results in quantitative form by means of Voronovskaja type theorems have been also established.
Convergence of generalized sampling series in weighted spaces
(De Gruyter Poland Sp Z O O, 2022) Acar, Tuncer; Alagoz, Osman; Aral, Ali; Costarelli, Danilo; Turgay, Metin; Vinti, Gianluca
The present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of continuity is presented and a quantitative Voronovskaja-type theorem is obtained.