Geodesic
Approximation by sampling-type nonlinear discrete operators in ϕ-variation
Filomat, Tome 35 (2021) no. 8, p. 2731

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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
DOI : 10.2298/FIL2108731A
Classification : 26A45, 40A25, 41A25, 47H99, 40C05
Keywords: Approximation in ϕ-variation, discrete operators, generalized sampling series, rate of approximaiton, summability process 
Ísmail Aslan. Approximation by sampling-type nonlinear discrete operators in ϕ-variation. Filomat, Tome 35 (2021) no. 8, p. 2731 . doi: 10.2298/FIL2108731A
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     author = {\'Ismail Aslan},
     title = {Approximation by sampling-type nonlinear discrete operators in \ensuremath{\phi}-variation},
     journal = {Filomat},
     pages = {2731 },
     year = {2021},
     volume = {35},
     number = {8},
     doi = {10.2298/FIL2108731A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2108731A/}
}
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