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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.

Rate of convergence of Szász-beta operators based on q-integers

Gupta P., Agrawal P. N.

Demonstratio Mathematica

2017

Vol. 50, nr 1

130--143

The purpose of this paper is to establish the rate of convergence in terms of the weighted modulus of continuity and Lipschitz type maximal function for the q-Szász-beta operators. We also study the rate of A-statistical convergence. Lastly, we modify these operators using King type approach to obtain better approximation.

On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev-Ibragimov operators

Ghorbanalizadeh A. M

Journal of Applied Analysis

2014

Vol. 20, nr 1

87--92

The generalization of Gadjiev–Ibragimov operators by means of Kantorovich and Kirov–Popova is considered and the order of weighted approximation of unbounded functions are obtained.