On translativity of absolute Riesz summability

In this work we characterize translativity of the summability | R , p n | k , k > 1 , for any sequence ( p n ) without imposing the conditions given by Orhan [C. Orhan, Translativity of absolute weighted mean summability, Czechoslovak Math. J. 48 (1998) 755–761], and so deduce some known results.