Summability factors for lower-semi-matrix transformations

In view of Kogbetliantz's identity 7] the absolute Cesáro 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 Cesáro mean of orderk of sequence {na _n }.Das 5] has shown that similar dependence is true for certain classes of Nörlund 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 Cesáro summability factors and a result ofBosanquet andDas 1] on absolute Harmonic summability factors.