Article
Summary:
In this paper, we give necessary and sufficient conditions on $(p_n)$ for $| R,p_n| _k$, $k\ge 1$, to be translative. So we extend the known results of Al-Madi [1] and Cesco $\left[ 4\right] $ to the case $k>1$.
References:
                        
[1] A. K. Al-Madi: 
On translativity of absolute weighted mean methods. Bull. Cal. Math. Soc. 79 (1987), 235–241. 
MR 0943202 | 
Zbl 0663.40003[2] W. Beekmann and K. Zeller: 
Theorie der Limitierungsverfahren. Springer-Verlag, Berlin-Heidelberg-New York, 1970. 
MR 0264267[4] R. P. Cesco: 
On the theory of linear transformations and the absolute summability of divergent series. Univ. Nac. La Plata. Publ. Fac. Cien. Fisicomat. Series 2, Revista 2 (1941), 147–156. 
MR 0007062[10] R. E. Powell and S. M. Shah: Summability Theory and Applications. Prentice-Hall of India, New Delhi, 1988.