On the Rate of Convergence of the Generalized Durrmeyer Type Operators for Functions of Bounded Variation

In this paper, we study the convergence in variation for the generalized sampling operators based upon averaged-type kernels and we obtain a characterization of absolutely continuous functions. This result is proved exploiting a relation between the first derivative of the above operator acting on $f$ and the sampling Kantorovich series of f'. By such approach, also a variation detracting-type property is established. Finally, examples of averaged kernels are provided, such as the central B-splines of order $n$ (duration limited functions) or other families of kernels generated by the Fejer and the Bochner-Riesz kernels (bandlimited functions).

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A characterization of the convergence in variation for the generalized sampling series

In this paper, we introduce Baskakov-Bezier operator B n , α which is an operator of probabilistic type We study the rate of convergence of the operator B n , α for locally bounded functions by using some inequalities and results of probability theory Our estimate is essentially the best possible

Rate of convergence of Baskakov-Bezier type operators for locally bounded functions

Bezier variant of a new durrmeyer type operators

On the Rate of Convergence of the Generalized Szász Type Operators for Functions of Bounded Variation

On the Rate of Convergence of Two Bernstein-Bézier Type Operators for Bounded Variation Functions, II

Rate of pointwise approximation for locally bounded functions by Szasz operators

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Alain Piriou

Papers

On the Rate of Convergence of Two Bernstein-Bézier Type Operators for Bounded Variation Functions, II

Rate of pointwise approximation for locally bounded functions by Szasz operators

Propagation et reflexion de la propriete de transmission des distributions de fourier

Hyperbolic conormal spaces and semilinear wave equation

On the nonlinear type singularities for semilinear Cauchy problems