On fractional differences, moduli of smoothness and best trigonometric approximation (Q1105799)

Some properties of differences of positive orders of Denjoy-integrable functions, estimations of modulus of smoothness, and some approximation theorems of Denjoy integrable functions are proved. In particular, some results of \textit{P. L. Butzer}, \textit{H. Dyckhoff}, \textit{E. Görlich}, \textit{R. L. Stens} [Can. J. Math. 29, 781-793 (1977; Zbl 0357.26003)] and \textit{R. Taberski} [Commentat. Math., Spec. Vol. II, dedic. L. Orlicz, 315-328 (1979; Zbl 0486.42002)] are extended to the case of Denjoy- integrable functions.