Asymptotic formulae for recursively defined Baskakov-type operators (Q2774632)

Altomare's Bari school has studied elliptic-parabolic equations by means of positive operators. We refer to the monograph [\textit{F. Altomare} and \textit{M. Campiti}, Korovkin-type approximation theory and its applications, de Gruyter, Berlin (1994; Zbl 0924.41001)]; see also [\textit{F. Altomare}, Ann. Scuola Norm. Super. Pisa, Cl. Sci. (4) 16, 259-279 (1989; Zbl 0706.47022)], [\textit{F. Altomare}, Conf. Semin. Mat. Univ. Bari 237-244, 57-82 (1991; Zbl 0789.47030)]. The author studies Baskakov-type operators pointing out new regularity properties. The main result is Voronovskaja-type formula where the second order derivative is perturbed by a term depending on two fixed sequences. Also a global approximation properties of such operators are given in some spaces of functions of polynomial growth.