Abstract The concept of Vilenkin–Lebesgue points was introduced in [12], where the almost everywhere convergence Fejer means Vilenkin–Fourier series proved. In this paper, we present a different (and simpler) approach to prove similar result, which can be used that corresponding result holds also more general context, namely for regular Norlund and T -means.

where the s{j are the partial sums of a double series EM»./> which remain bounded for all (i, j). The necessary and sufficient conditions for regularity of Norlund means in the case of such double series have been given by C. N. Moore in Theorem II of Chapter II of his book4 entitled Summable series and convergence factors which will be subsequently referred to as S.S.C.F. In the case where the...

in this paper, the notion of n, pn - summability to generalize the concept of statisticalconvergence is used. we call this new method weighted statistically convergence. we also establish itsrelationship with statistical convergence, c,1-summability and strong   n n, p -summability.