Previous |  Up |  Next

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
[3] H. Bor: On the relative strength of two absolute summability methods. Proc. Amer. Math. Soc. 113 (1991), 1009–1012. DOI 10.1090/S0002-9939-1991-1068115-X | MR 1068115 | Zbl 0743.40007
[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
[5] G. G. Cooke: Infinite Matrices and Sequence Spaces. Macmillan Co., London, 1950. MR 0040451 | Zbl 0040.02501
[6] J. A. Fridy: Abel transformations into $l^1$. Canad. Math. Bull. 25 (1982), 421–427. DOI 10.4153/CMB-1982-060-5 | MR 0674557
[7] B. Kuttner and B. Thorpe: Translativity of some absolute summability methods. Analysis 14 (1994), 57–65. DOI 10.1524/anly.1994.14.1.57 | MR 1280529
[8] F. M. Mears: Absolute regularity and Nörlund mean. Annals of Math. 38 (1937), 594–601. DOI 10.2307/1968603 | MR 1503356
[9] C. Orhan: On equivalence of summability methods. Math. Slovaca 40 (1990), 171–175. MR 1094771 | Zbl 0736.40002
[10] R. E. Powell and S. M. Shah: Summability Theory and Applications. Prentice-Hall of India, New Delhi, 1988.
Partner of
EuDML logo