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

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 summability for an infinite series. We further obtained well-known applications of the above theorem as corollaries, under suitable conditions.

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].…”

Approximation of a Function Belonging to Lip (ɑ, θ, w) by (C, 1) (E, q)

“…Recently, Sonker and Munjal [18][19][20][21][22][23][24][25] gave a number of theorems exploring summability of the Orthogonal, Fourier series and infinite series. In the present result, summability method has been used for sharper estimations.…”