Summability factors for lower-semi-matrix transformations

Abstract

In view of Kogbetliantz's identity [7] the absolute Cesaro summability of orderk (k)>−1) of an infinite seriesΣ a n is the same as the absolute convergence ofΣ(τ n k )n−1 whereτ n k is then-th Cesaro mean of orderk of sequence {na n }.Das [5] has shown that similar dependence is true for certain classes of Norlund means. The object of this paper is to establish two theorems on absolute summability factors involving two lower-semimatrix transformations and thereby to generalise a result ofChow [3] on absolute Cesaro summability factors and a result ofBosanquet andDas [1] on absolute Harmonic summability factors.