Abstract
In this paper, we construct a new general class of operators which have the classical Szász Mirakyan ones as a basis, and fix the functions \(e^{ax}\) and \(e^{2ax}\) with \(a>0\). The convergence of the corresponding sequences is discussed in exponential weighted spaces, and a Voronovskaya type result is given. Also we define a new weighted modulus of smoothness and determine the approximation order of the constructed operators. Finally, we study the goodness of the estimates of our new operators via saturation results.
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Acar, T., Aral, A., Cárdenas-Morales, D. et al. Szász–Mirakyan Type Operators Which Fix Exponentials. Results Math 72, 1393–1404 (2017). https://doi.org/10.1007/s00025-017-0665-9
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DOI: https://doi.org/10.1007/s00025-017-0665-9