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.
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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.
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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.
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