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Convergence of generalized sampling series in weighted spaces

Acar Tuncer, Alagöz Osman, Aral Ali, Costarelli Danilo, Turgay Metin, Vinti Gianluca

Demonstratio Mathematica

2022

Vol. 55, nr 1

153--162

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.

Voronovskaja-type theorems and approximation theorems for a class of GBS operators

Pop O. T.

Fasciculi Mathematici

2009

Nr 42

91-108

In this paper we will demonstrate a Voronovskajatype theorems and approximation theorems for GBS operators associated to some linear positive operators. Through parti- cular cases, we obtain statements verified by the GBS operators of Bernstein, Schurer, Durrmeyer, Kantorovich, Stancu, Bleimann- Butzer-Hahn, Mirakjan-Favard-Szász, Baskakov, Meyer-König and Zeller, Ismail-May.