Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces

Year 2021, Volume: 4 Issue: 2, 229 - 241, 01.06.2021

Laura Angelonı , Nursel Çetin , Danilo Costarellı , Anna Rita Sambucını , Gianluca Vıntı

https://doi.org/10.33205/cma.876890

Cited By: 11

Abstract

In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.

Keywords

Multivariate sampling Kantorovich operators, Orlicz spaces, modulus of smoothness, quantitative estimates, Lipschitz classes

Supporting Institution

University of Perugia Ricerca di Base (2017,2018), Gnampa-Indam (2020), Fondazione Cassa di Risparmio di Perugia (2018,2019)

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