Summability process by Mastroianni operators and their generalizations (Q2018690)

The author studies the approximation properties of operators, called modified Mastroianni operators, which are obtained by applying the \(A\)-summability methods introduced in [\textit{H.T. Bell}, Proc. Am. Math. Soc. 38, 548--552 (1973; Zbl 0259.40003)] to the Mastroianni operators introduced by \textit{G. Mastroianni} in [Rend. Accad. Sci. Fis. Mat., IV. Ser., Napoli 46, 161--176 (1979; Zbl 0452.41018)]. It is proven that, under some assumptions on \(A\) and the decay rate of \(f\), the modified Mastroianni operators applied to \(f\) converge uniformly to \(f\) on compact subsets of \([0,\infty)\). Upper bounds on the error of approximation are also given in terms of the modulus of smoothness. A Voronovskaya-type theorem is also proven for a specific choice of \(A\).