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On the rate of convergence of some integral operators for functions of bounded variation

Abstract


In the present paper we define a general class \(B_{n,\alpha},\alpha\) \(\geq1\), of Durrmeyer-Bezier type of linear positive operators. Our main aim is to estimate the rate of pointwise convergence for functions \(f\) at those points\(x\) at which the one-sided limits \(f\left(x+\right)\) and \(f\left(x-\right)\) exist. As regards these functions defined on an interval \(J\) certain conditions are required. We discuss two distinct cases: Int \(\left( J\right) =\left(0,\infty\right)\) and (\left( J\right)=0,1\).

Authors

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Approximation process; function with bounded variation; Kantorovich-type operators; rate of convergence.

Paper coordinates

O. Agratini, On the rate of convergence of some integral operators for functions of bounded variation, Studia Scientiarum Mathematicarum Hungarica, 42 (2005)  no. 2, pp. 235-252, https://doi.org/10.1556/sscmath.42.2005.2.8

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Studia Scientiarum Mathematica Hungarica

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2005

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