Abstract
It is shown in [4] that if a normal matrix,A satisfies some conditions then |C,1| k summability implies |A| k summability wherek≥1. In the present paper, we consider the converse implication.
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References
Flett T M, On an extension of absolute summability and theorems of Littlewood and Paley,Proc. London Math. Soc. 7 (1957) 113–141
Cooke R G,Infinite Matrices and Sequence Spaces (Macmillan) (1950)
Kogbetliantz E, Sur les series absolument sommables par la methode des moyennes arithmetiques,Bull. Sci. Math. 49 (1925) 234–256
Orhan C, On absolute summability,Bull. Inst. Math. Acad. Sinica 15 (1987) 433–437
Orhan C, On equivalence of summability methods,Math. Slovaca 40 (1990) 171–175
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Orhan, C., Sarigöl, M.A. Absolute summability of infinite series. Proc. Indian Acad. Sci. (Math. Sci.) 105, 201–205 (1995). https://doi.org/10.1007/BF02880366
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DOI: https://doi.org/10.1007/BF02880366