Sharpening of Stečkin's theorem to strong approximation (Q1813304)

The author gives a theorem on strong approximation of a function by de la Vallee Poussin means. The theorem proved here improves upon, among other results, some results of \textit{S. B. Stechkin} [Ann. Math. 4, 61-74 (1978; Zbl 0393.41009)] and \textit{V. Totik} [Acta Math. Acad. Sci. Hung. 35, 151- 172 (1980; Zbl 0454.42001)]. It is given that the result is the best possible in a certain sense. The author has well introduced the problem providing adequate information on the background materials.