A new note on absolute matrix summability

Abstract

In the present paper, we have proved theorems dealing with matrix summability factors by using quasi β-power increasing sequences. Some new results have also been obtained. MSC: 40D15; 40F05; 40G99

A new result on the quasi power increasing sequences

“…There are some papers on absolute matrix summability (see [10,11,12,13,15,16,17,18,19,20]). The aim of this paper is to obtain a theorem dealing with the absolute matrix summability of infinite series.…”

“…Therefore, by using Abel's transformation, and (11), (2), (14), (13) we obtain If we take (X n ) as an almost increasing sequence and ϕ n = Pn pn , then we get a theorem dealing with |A, p n | k summability (see [10]). Also, if we take (X n ) as a positive non-decreasing sequence, ϕ n = n, a nv = pv Pn and p n = 1 for all values of n, then we get a theorem dealing with |C, 1| k summability (see [8]).…”

SPECTRA OF THE LOWER TRIANGULAR MATRIX B(r1, . . . , rl ; s1, . . . , sl ′) OVER c0

“…Furkan and Bilgiç studied B(r, s) in the same direction over ℓ p and bv p in [6]. For more study, we refer [2,7,8,12,13,18,19,22,24] etc. Now if one considers the more generalized difference matrix whose diagonal and subdiagonal entries are the oscillatry sequences (r 1 , r 2 , .…”