Some inequalities related to strongconvergence of Riesz logarithmic means

In this paper we derive a new strong convergence theorem of Riesz logarithmicmeans of the one-dimensional Vilenkin–Fourier (Walsh–Fourier) series. Thecorresponding inequality is pointed out and it is also proved that the inequality is in asense sharp, at least for the case with Walsh–Fourier series