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Absolute summability factors of infinite series. (English) Zbl 0932.40006
H. Bor [On absolute summability factors, Proc. Am. Math. Soc. 118, No. 1, 71-75 (1993; Zbl 0784.40003)] proved the $|\overline{N},{p}_{n}{|}_{k}$, $k\ge 1$ summability of the series $\sum {a}_{n}{\lambda }_{n}$ under certain conditions which extends the previous result of Mazhar on the ${|C,1|}_{k}$, $k\ge 1$ summability of $\sum {a}_{n}{\lambda }_{n}$; see S. M. Mazhar [Indian J. Math. 14, 45-48 (1972; Zbl 0253.42008)]. In the present paper Mazhar proves the $|\overline{N},{p}_{n}{|}_{k}$, $k\ge 1$ summability of $\sum {a}_{n}{\lambda }_{n}$ which generalizes the above-mentioned result of H. Bor.

MSC:
 40F05 Absolute and strong summability 40D15 Convergence factors; summability factors 40D25 Inclusion theorems; equivalence theorems
Keywords:
summability factors; series