Approximation by multivariate Baskakov–Kantorovich operators in Orlicz spaces

Ling-Xiong Han; Wen-Hui Li; Feng Qi; Ling-Xiong Han; Wen-Hui Li; Feng Qi

doi:10.3934/era.2020037

Electronic Research Archive

2020, Volume 28, Issue 2: 721-738. doi: 10.3934/era.2020037

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Approximation by multivariate Baskakov–Kantorovich operators in Orlicz spaces

Ling-Xiong Han ^{1
,},
Wen-Hui Li ^{2
,},
Feng Qi ^{3
,
,}

1.
College of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, China
2.
Department of Fundamental Courses, Zhengzhou University of Science and Technology, Zhengzhou 450064, Henan, China
3.
Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, China, School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China

Received: 01 January 2020 Revised: 01 March 2020
Primary: 41A17; Secondary: 41A36

Utilizing some properties of multivariate Baskakov–Kantorovich operators and using $ K $-functional and a decomposition technique, the authors find two equivalent theorems between the $ K $-functional and modulus of smoothness, and obtain a direct theorem in the Orlicz spaces.
- Equivalent theorem,
- direct theorem,
- approximation,
- multivariate Baskakov–Kantorovich operator,
- Orlicz space,
- Jensen's inequality,
- $K$-functional
Citation: Ling-Xiong Han, Wen-Hui Li, Feng Qi. Approximation by multivariate Baskakov–Kantorovich operators in Orlicz spaces[J]. Electronic Research Archive, 2020, 28(2): 721-738. doi: 10.3934/era.2020037

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Abstract

Utilizing some properties of multivariate Baskakov–Kantorovich operators and using $ K $-functional and a decomposition technique, the authors find two equivalent theorems between the $ K $-functional and modulus of smoothness, and obtain a direct theorem in the Orlicz spaces.

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