Summability factor relations between absolute weighted and Cesaro means

By (U, V), we denote the set of all sequences epsilon = (epsilon(n)) such that Sigma epsilon(n)a(n) is summable V whenever Sigma a(n) is summable U, where U and V are two summability methods. Recently, Sarigol has characterized the set (vertical bar C, alpha vertical bar(k), vertical bar(N) over bar, p(n)vertical bar) for k > 1, alpha > -1 and arbitrary positive sequences (p(n)). Now, in the present paper, we characterize the sets (vertical bar C, -1 vertical bar(k), vertical bar(N) over bar, p(n)vertical bar), k > 1 and (vertical bar(N) over bar, p(n)vertical bar, vertical bar C, -1 vertical bar(k)), k >= 1 for arbitrary positive sequences (p(n)). Hence we extend these results to the range alpha >= -1. In this way, some open problems in this topic are also completed.C1 [Gulec, Gullu Canan Hazar] Pamukkale Univ, Dept Math, TR-20070 Denizli, Turkey