On a new application of almost increasing sequences

Abstract

In (Bor in Int. J. Math. Math. Sci. 17:479-482, 1994), Bor has proved the main theorem dealing with |N, p n | k summability factors of an infinite series. In the present paper, we have generalized this theorem on the ϕ -|A, p n | k summability factors under weaker conditions by using an almost increasing sequence instead of a positive non-decreasing sequence. MSC: 40D15; 40F05; 40G99

A Study on Generalized Absolute Matrix Summability

“…There are many studies on absolute matrix summability of infinite series [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. This study provides a generalization of above mentioned theorem to…”

Necessary and sufficient conditions for the inclusion relation between two summability methods

“…Sezer and Çanak [20], Bor [2] obtained equivalence theorems on summability. Özgen [19], Özarslan and Karakaş [14], Özarslan and Kartal [15], [17], Sonker and Munjal [21], [22], Karakaş [7], Kartal [8], [9], Özarslan [10], [11], Bor and Agarwal [3], Bor and Mohapatra [4] obtained theorems on absolute Riesz, Cesàro and matrix summability of infinite series. Furthermore, the following theorem on the relative strength of two absolute matrix summability methods has been proved in [13].…”

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.…”