İsmail Aslan
Approximation by sampling-type nonlinear discrete operators in Phi-variation, Filomat, 35(8), 2731-2746, 2021

In the present paper, our purpose is to obtain a nonlinear approximation by using convergence

in φ-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 φ-absolutely continuous functions. Finally, we give some examples of kernels, which fulfill our

kernel assumptions.