Abstract
A modification of Szász–Mirakyan operators is presented that reproduces the functions 1 and \(e^{2ax}\), \(a>0\) fixed. We prove uniform convergence, order of approximation via a certain weighted modulus of continuity, and a quantitative Voronovskaya-type theorem. A comparison with the classical Szász–Mirakyan operators is given. Some shape preservation properties of the new operators are discussed as well. Using a natural transformation, we also present a uniform error estimate for the operators in terms of the first- and second-order moduli of smoothness.
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Acar, T., Aral, A. & Gonska, H. On Szász–Mirakyan Operators Preserving \(\varvec{e^{2ax}},\) \(\varvec{a>0}\) . Mediterr. J. Math. 14, 6 (2017). https://doi.org/10.1007/s00009-016-0804-7
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DOI: https://doi.org/10.1007/s00009-016-0804-7