A New Application of Almost Increasing Sequences

Abstract

Bor has proved a main theorem dealing with |N , 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.Mathematics Subject Classification 2010: 40D25, 40F05, 40G99.

Local properties of absolute matrix summability of factored fourier series

“…Let (ϕ n ) be any sequence of positive real numbers. The series a n is said to be summable ϕ − A, p n k , k ≥ 1, if (see [26])…”

A generalization of a theorem of Bor

“…At that time T describes the sequence-to-sequence transformation, mapping the sequence to , where Let be any sequence of positive real numbers. The series is said to be summable , , if (see [ 3 ]) where If we take , then summability reduces to summability (see [ 4 ]). If we set for all n , summability is the same as summability (see [ 5 ]).…”