Abstract
In the present paper, we introduce q-analogue of the Jakimovski–Leviatan operators with the help of q-Appell polynomials. We establish some moments and auxiliary results by using q-derivatives and then prove a basic convergence theorem. Also, the Voronovskaja-type asymptotic formula and some direct results for the above operators are discussed. Moreover, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied.
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The second author would like to express his gratitude to King Khalid University, Abha, Saudi Arabia for providing administrative and technical support.
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Mursaleen, M., Ansari, K.J. & Nasiruzzaman, M. Approximation by q-analogue of Jakimovski–Leviatan operators involving q-Appell polynomials. Iran J Sci Technol Trans Sci 41, 891–900 (2017). https://doi.org/10.1007/s40995-017-0331-9
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DOI: https://doi.org/10.1007/s40995-017-0331-9