Approximation by Sampling-type Nonlinear Discrete Operators In Phi-variation

Abstract

In the present paper, our purpose is to obtain a nonlinear approximation by
using convergence in $\varphi$-variation. Angeloni and Vinti prove some
approximation results considering linear sampling-type discrete operators.
These types of operators have close relationships with generalized sampling
series. By improving Angeloni and Vinti's one, we aim to get a nonlinear
approximation which is also generalized by means of summability process. We
also evaluate the rate of approximation under appropriate Lipschitz classes of
$\varphi$-absolutely continuous functions. Finally, we give some examples of
kernels, which fulfill our kernel assumptions.