Summability factor relations between absolute weighted and Cesàro means

ByU , V , we denote the set of all sequences ϵ =ϵ nsuch that Σ ϵ n a n is summable V whenever Σ a n is summable U , where U and V are two summability methods. Recently, Sarıgöl has characterized the setC , αk ,N ‾ , p nfor k   >  1, α   >  −1 and arbitrary positive sequencesp n. Now, in the present paper, we characterize the setsC , − 1k ,N ‾ , p n, k   >  1 andN ‾ , p n,C , − 1k, k   ≥  1 for arbitrary positive sequencesp n. Hence we extend these results to the range α ≥ − 1. In this way, some open problems in this topic are also completed.