AIMS Mathematics, 2020, 5(4): 3019-3034. doi: 10.3934/math.2020196.

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

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

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.
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Keywords 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. AIMS Mathematics, 2020, 5(4): 3019-3034. doi: 10.3934/math.2020196


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