New results for almost increasing sequences

Abstract

In the present paper, two theorems of absolute summability have been proved by using the definition of almost increasing sequence.

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].…”