Approximation by semi-exponential Post-Widder operators (Q6630767)

The so-called ``exponential operators'', introduced in [\textit{C. P. May}, Can. J. Math. 28, 1224--1250 (1976; Zbl 0342.41018)] were intensively investigated in Approximation Theory. They were generalized in [\textit{A. Tyliba} and \textit{E. Wachnicki}, Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 45, No. 1, 59--73 (2005; Zbl 1096.41016)]. \textit{M. Herzog} in [Symmetry 13, No. 4, Paper No. 637, 10 p. (2021; \url{doi:10.3390/sym13040637})] named these generalized operators as ``semi-exponential operators'' and studied their approximation properties for functions belonging to exponential weighted spaces. \N\NThe present article is devoted to the approximation properties of semi-exponential Post-Widder operators associated with a quadratic polynomial. The authors obtain the rate of convergence of these operators for continuous and bounded functions in terms of the modulus of continuity. They prove Voronovskaya-type approximation theorems in polynomial weighted spaces. Furthermore, some direct estimates are also obtained for Lipschitz-type function spaces.