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    On Szasz-Mirakyan Operators Preserving e(2ax), a > 0
    (Springer Basel Ag, 2017) Acar, Tuncer; Aral, Ali; Gonska, Heiner
    A modification of Szasz-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 Szasz-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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    Quantitative Voronovskaya-Type Results for Polynomially Bounded Functions
    (Springer Basel Ag, 2016) Aral, Ali; Gonska, Heiner; Heilmann, Margareta; Tachev, Gancho
    We prove quantitative Voronovskaya-type results and Gruss-Voronovskaya inequalities for polynomially bounded functions. The results are given in terms of suitable K-functionals and applied to linking Szasz-Mirakyan and Baskakov operators.