On Absolute Summability Factors

Abstract

By using for $\delta \ge 0$ so-called $|\bar{N},p_n;\delta {|}_k$-boundedness of series ${\sum }_{n=1}^{\infty }{a}_n$ and sequences $({\lambda }_n{)}_{n=1}^{\infty }$ we prove $|\bar{N},p_n;\delta {|}_k$-summability of the series ${\sum }_{n=1}^{\infty }{a}_n{\lambda }_n$. This result generalizes a known one related to $|\bar{N},p_n{|}_k$-summability of series.