Absolute matrix summability via almost increasing sequence

A Note on Summability of Infinite Series

“…Let us mention about some of the recent ones. Karakaş [5,6] , Kartal [7,8], Özarslan [9][10][11][12], Özarslan and Kartal [13,14], Özarslan, Şakar and Kartal [15] proved theorems on the sufficient conditions to absolute matrix summability of infinite series by using different class of sequences. The object of this paper is to get the necessary and sufficient conditions to absolute matrix summability.…”

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].…”