On the convergence of Ces\'aro means of negative order of Vilenkin-Fourier series

Abstract

In 1971 Onnewer and Waterman establish sufficient condition which guarantees uniform convergence of Vilenkin-Fourier series of continuous function. In the paper we consider different classes of functions of generalized bounded oscilation and in the terms of these classes there are established sufficient conditions for uniform convergence of Ces\'aro means of negative order.