Absolute weighted arithmetic mean summability factors of infinite series and trigonometric fourier series

In this paper, we generalized a known theorem dealing with absolute weighted arithmetic mean summability of infinite series by using a quasi-f-power increasing sequence instead of a quasi-?-power increasing sequence. And we applied it to the trigonometric Fourier series

Generalized quasi power increasing sequences and their some new applications

In this paper, we generalize a known theorem by using a general class of power increasing sequences instead of a quasi-?-power increasing sequence. This theorem also includes some known and new results.

A new theorem on the absolute Riesz summability factors

In [5], we proved a main theorem dealing with absolute Riesz summability factors of infinite series using a quasi-?-power increasing sequence. In this paper, we generalize that theorem by using a general class of power increasing sequences instead of a quasi-?-power increasing sequence. This theorem also includes some new and known results.

Power Increasing Sequences and Their Some New Applications

In the work of Bor (2008), we have proved a result dealing with summability factors by using a quasi--power increasing sequence. In this paper, we prove that result under less and more weaker conditions. Some new results have also been obtained.

A new application of certain generalized power increasing sequences

The main object of this paper is to prove two general theorems by using a two-parameter quasi- f (?,?) -power increasing sequence instead of a quasi-?-power increasing sequence. The first result (Theorem 2.1) in this paper covers the case when 0 < ? < 1 and ? = 0. The second main result (Theorem 2.3) in this paper covers the exceptional case when ? = 1 and ? 5 0. Each of these theorems also includes several new or known results as their special cases and consequences.