Approximation of Jakimovski-Leviatan-Beta type integral operators via <em>q</em>-calculus

Abdullah Alotaibi; M. Mursaleen; Abdullah Alotaibi; M. Mursaleen

doi:10.3934/math.2020196

AIMS Mathematics

2020, Volume 5, Issue 4: 3019-3034. doi: 10.3934/math.2020196

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Research article

Approximation of Jakimovski-Leviatan-Beta type integral operators via q-calculus

Abdullah Alotaibi ¹,
M. Mursaleen ^{2,3,4
,
,}

1.
Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
2.
Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan
3.
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
4.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

Received: 22 November 2020 Accepted: 13 March 2020 Published: 20 March 2020
MSC : Primary: 41A2, 41A36; Secondary: 33C45

We construct Jakimovski-Leviatan-Beta type q-integral operators and show that these positive linear operators are uniformly convergent to a continuous functions. We obtain the Korovkin type results, the rate of convergence as well as some direct theorems.
- Appell polynomials,
- q-Appell polynomials,
- Jakimovski-Levitian operators,
- Jakimovski-Leviatan-Beta operators,
- Korovkin’s theorem,
- modulus of continuity
Citation: Abdullah Alotaibi, M. Mursaleen. Approximation of Jakimovski-Leviatan-Beta type integral operators via q-calculus[J]. AIMS Mathematics, 2020, 5(4): 3019-3034. doi: 10.3934/math.2020196

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Abstract

We construct Jakimovski-Leviatan-Beta type q-integral operators and show that these positive linear operators are uniformly convergent to a continuous functions. We obtain the Korovkin type results, the rate of convergence as well as some direct theorems.

References

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