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Approximation properties of Szasz-Mirakyan operators preserving exponential functions
(Springer, 2019) Aral, Ali; Inoan, Daniela; Rasa, Ioan
This paper is a natural continuation of Acar et al. (Mediterr J Math 14:6, 2017, 10.1007/s00009-016-0804-7) where Szasz-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.
On differences of linear positive operators
(Springer Basel Ag, 2019) Aral, Ali; Inoan, Daniela; Rasa, Ioan
In this paper we consider two different general linear positive operators defined on unbounded interval and obtain estimates for the differences of these operators in quantitative form. Our estimates involve an appropriate K-functional and a weighted modulus of smoothness. Similar estimates are obtained for Chebyshev functional of these operators as well. All considerations are based on rearrangement of the remainder in Taylor's formula. The obtained results are applied for some well known linear positive operators.