Approximation properties of modified (<em>p, q</em>)-Szász-Mirakyan-Kantorovich operators

Zhongbin Zheng; Jinwu Fang; Wentao Cheng; Zhidong Guo; Xiaoling Zhou; Zhongbin Zheng; Jinwu Fang; Wentao Cheng; Zhidong Guo; Xiaoling Zhou

doi:10.3934/math.2020317

AIMS Mathematics

2020, Volume 5, Issue 5: 4959-4973. doi: 10.3934/math.2020317

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Research article

Approximation properties of modified (p, q)-Szász-Mirakyan-Kantorovich operators

1.
China Academy of Information and Communications Technology, Shanghai 200232, China
2.
Industrial Internet Innovation Center (Shanghai) Co., Ltd., Shanghai, 200120, China
3.
School of Mathematics and Physics, Anqing

Received: 21 March 2020 Accepted: 09 May 2020 Published: 05 June 2020
MSC : 41A10, 41A25, 41A36

In this paper, we introduce a new kind of modified (p, q)-Szász-Mirakyan-Kantorovich operators based on (p, q)-calculus. Next, the moments computation formulas, the second and fourth order central moments computation formulas and other quantitative properties are investigated. Then, the approximation properties including local approximation, weighted approximation, rate of convergence and Voronovskaja type theorem are obtained. Finally, we generalize the operators by adding a parameter λ.
- modified (p, q)-Szász-Mirakyan-Kantorovich operators,
- moduli of continuity,
- rate of convergence,
- weighted approximation
Citation: Zhongbin Zheng, Jinwu Fang, Wentao Cheng, Zhidong Guo, Xiaoling Zhou. Approximation properties of modified (p, q)-Szász-Mirakyan-Kantorovich operators[J]. AIMS Mathematics, 2020, 5(5): 4959-4973. doi: 10.3934/math.2020317

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Abstract

In this paper, we introduce a new kind of modified (p, q)-Szász-Mirakyan-Kantorovich operators based on (p, q)-calculus. Next, the moments computation formulas, the second and fourth order central moments computation formulas and other quantitative properties are investigated. Then, the approximation properties including local approximation, weighted approximation, rate of convergence and Voronovskaja type theorem are obtained. Finally, we generalize the operators by adding a parameter λ.

References

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