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On the rates of convergence of certain bivariate linear positive operators

Olgun A, Taşdelen F.

Fasciculi Mathematici

2014

Nr 52

117--129

In this paper, we present a sequence of linear positive bivariate operators and investigate the approximation properties of them. Next we study the rates of converge of this approximation by means modulus of continuity and functions from Lipschitz class. After we give a Voronovskaya type theorem for n Morever, we give an r th order generalization of these operators. Finally, we investigate approximation properties of this generalization and observe the rates of convergence for them.

Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces

Costarelli D., Vinti G.

Commentationes Mathematicae

2013

Vol. 53, No. 2

171--192

In this paper, we study the rate of approximation for the nonlinear sampling Kantorovich operators. We consider the case of uniformly continuous and bounded functions belonging to Lipschitz classes of the Zygmund-type, as well as the case of functions in Orlicz spaces. We estimate the aliasing errors with respect to the uniform norm and to the modular functional of the Orlicz spaces, respectively. The general setting of Orlicz spaces allows to deduce directly the results concerning the rate of convergence in Lp-spaces, 1 ≤ p < ∞, very useful in the applications to Signal Processing. Others examples of Orlicz spaces as interpolation spaces and exponential spaces are discussed and the particular cases of the nonlinear sampling Kantorovich series constructed using Fejér and B-spline kernels are also considered.