Recently, we have proved a main theorem dealing with the absolute Nörlund summability factors of infinite series by using -quasimonotone sequences. In this paper, we prove that result under weaker conditions. A new result has also been obtained.
In this paper, we generalize a known theorem dealing with |C,?|k
summability factors to the |C,?,?,?|k summability factors of infinite
series. This theorem also includes some known and new results.
Abstract
Bor has proved a main theorem dealing with | N̄ , pn|k summability factors of infinite series. In this paper, we have generalized this theorem to the φ − |A, pn|k summability factors, under weaker conditions by using an almost increasing sequence instead of a positive monotonic non-decreasing sequence.
UDC 517.54
The aim of the paper is a generalization, under weaker conditions, of the main theorem on quasi-
σ
-power increasing sequences applied to
|
A
,
θ
n
|
k
summability factors of infinite series and Fourier series. We obtain some new and known results related to basic summability methods.
Abstract
In this paper, a known result dealing with | ̄N, pn|k summability of infinite series has been generalized to the φ − | ̄N, pn; δ|k summability of infinite series by using an almost increasing sequence.
Quasimonotone and Almost Increasing Sequences and Their New Applications
