Research PaperNo Access

The $L_{p}$ -saturation of linear combinations of Szász–Mirakjan–Kantorovich operators

Shuli Wang

Department of Mathematics, Lishui University, Lishui, Zhejiang 323000, P. R. China

Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

E-mail Address: sli.wang@qq.com

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and

Linsen Xie

https://orcid.org/0000-0002-9156-7453

Department of Mathematics, Lishui University, Lishui, Zhejiang 323000, P. R. China

E-mail Address: linsenxie@lsu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0219691324500462Cited by:0 (Source: Crossref)

Abstract

In this paper, we investigate the $L_{p}$ -saturation of linear combinations of Szász–Mirakjan–Kantorovich operators. The main difficulty is how to tackle the differential operators deduced by Szász–Mirakjan–Kantorovich operators. We firstly investigate the regularity of these differential operators. By virtue of the regularity, the saturation theorem for linear combinations of Szász–Mirakjan–Kantorovich operators is ultimately obtained. Namely, the $L_{p}$ -saturation class of these combinations is characterized.

Keywords:

AMSC: 40A25, 40H05, 43A15, 46A32, 47L05

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