Approximation properties of Szász–Mirakyan operators preserving exponential functions
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This paper is a natural continuation of Acar et al. (Mediterr J Math 14:6, 2017, https://doi.org/10.1007/s00009-016-0804-7) where Szász–Mirakyan operators preserving exponential functions are defined. As a first result, we show that the sequence of the norms of the operators, acting on weighted spaces having different weights, is uniformly bounded. Then, we prove Korovkin type approximation theorems through exponential weighted convergence. The uniform weighted approximation errors of the operators and their derivatives are characterized for exponential weights. Furthermore we give a Voronovskaya type theorem for the derivative of the operators.
KeywordsSzász–Mirakyan operators Weighted modulus of continuity Uniform convergence Voronovskaya type theorem
Mathematics Subject Classification41A25 41A36
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