Approximation properties of Stancu type Szász-Mirakjan operators

Bo-Yong Lian; Qing-Bo Cai; Bo-Yong Lian; Qing-Bo Cai

doi:10.3934/math.20231110

AIMS Mathematics

2023, Volume 8, Issue 9: 21769-21780. doi: 10.3934/math.20231110

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Approximation properties of Stancu type Szász-Mirakjan operators

Bo-Yong Lian ^{1
,
,},
Qing-Bo Cai ²

1.
Department of Mathematics, Yang-en University, Quanzhou 362000, China
2.
School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China

Received: 16 May 2023 Revised: 25 June 2023 Accepted: 29 June 2023 Published: 10 July 2023
MSC : 41A10, 41A25, 41A36

In this paper, a class of Stancu type Szász-Mirakjan operators are introduced. The approximation properties of the operators are discussed using tools of modulus of continuity, modulus of smoothness and K-functional. The estimation of the Lipschitz function class by the operators is also studied. Later, the Voronvskaya type asymptotic expansion of the operators is established. Finally, we compare the convergence of these newly defined operators for certain functions with certain graphs.
- Szász-Mirakjan operators,
- modulus of continuity,
- K-functional,
- Voronovskaya-type asymptotic formula,
- rate of convergence
Citation: Bo-Yong Lian, Qing-Bo Cai. Approximation properties of Stancu type Szász-Mirakjan operators[J]. AIMS Mathematics, 2023, 8(9): 21769-21780. doi: 10.3934/math.20231110

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Abstract

In this paper, a class of Stancu type Szász-Mirakjan operators are introduced. The approximation properties of the operators are discussed using tools of modulus of continuity, modulus of smoothness and K-functional. The estimation of the Lipschitz function class by the operators is also studied. Later, the Voronvskaya type asymptotic expansion of the operators is established. Finally, we compare the convergence of these newly defined operators for certain functions with certain graphs.

References

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