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Quantitative Estimates for Nonlinear Sampling Kantorovich Operators
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Journal Article
Quantitative Estimates for Nonlinear Sampling Kantorovich Operators
2021
Overview
In this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of smoothness in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative estimates of approximation in
L
p
-spaces,
1
≤
p
<
∞
, and in other well-known instances of Orlicz spaces, such as the Zygmung and the exponential spaces. Further, the qualitative order of approximation has been obtained assuming
f
in suitable Lipschitz classes. The above estimates achieved in the general setting of Orlicz spaces, have been also improved in the
L
p
-case, using a direct approach suitable to this context. At the end, we consider the particular cases of the nonlinear sampling Kantorovich operators constructed by using some special kernels.
Publisher
Springer International Publishing,Springer Nature B.V
Subject
