Absolute φ − | C , α , β ; δ | k $\varphi- \vert C, \alpha, \beta; \delta\vert _{k}$ summability of infinite series

Abstract

Abstract In this paper, we established a generalized theorem on a minimal set of sufficient conditions for absolute summability factors by applying a sequence of a wider class (quasi-power increasing sequence) and the absolute Cesàro φ − | C , α , β ; δ | k $\varphi-\vert C, \alpha, \beta; \delta \vert _{k}$ summability for an infinite series. We further obtained well-known applications of the above theorem as corollaries, under suitable conditions.

Keywords

• absolute summability
• infinite series
• φ − | C , α , β ; δ | k $\varphi- \vert C, \alpha, \beta; \delta \vert _{k}$ summability
• quasi-f-power increasing sequence