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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.

The voronovskaja type theorem for an extension of Szász-Mirakjan operators

Pop O. T., Bărbosu D., Miclăus D.

Demonstratio Mathematica

2012

Vol. 45, nr 1

107-115

Recently ,C.Mortici defined a class of linear and positive operators depending on a certain function (…) which generalize the well known Szasz Mirakjan operators. For these generalized operators we establish a Voronovskaja type theorem, the uniform convergence and the order of approximation, using the modulus of continuity.

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.

About some linear and positive operators defined by infinite sum

Pop O.

Demonstratio Mathematica

2006

Vol. 39, nr 2

377-388

In [13], we study a class of linear and positive operators defined by finite sum. In this paper we demonstrate general properties for a class of linear positive operators denned by infinite sum. By particularization, we obtain statements, the convergence and the evaluation for the rate of convergence in therm of the first modulus of smoothness for the Mirakjan-Favard-Szasz operators, Baskakov operators and Mayer-Konig and Zeiler operators. We don't study the convergence of these operators with the well known theorem of Bohman-Korowkin.