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Absolute summability factors of infinite series. (English) Zbl 0932.40006
{\it 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 {\it 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.

40F05Absolute and strong summability
40D15Convergence factors; summability factors
40D25Inclusion theorems; equivalence theorems