Abstract

In this paper, a general theorem concerning absolute matrix summability is established by applying the concepts of almost increasing and δ-quasi-monotone sequences.

Highlights

  • A positive sequence is said to be almost increasing if there is a positive increasing sequence and two positive constants K and M such that Kun ≤ yn ≤ Mun

  • In this paper, a general theorem concerning absolute matrix summability is established by applying the concepts of almost increasing and δ-quasi-monotone sequences

  • 2 Known result In [, ], Bor has established the following theorem dealing with |N, pn|k summability factors of infinite series

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Summary

Introduction

A positive sequence (yn) is said to be almost increasing if there is a positive increasing sequence (un) and two positive constants K and M such that Kun ≤ yn ≤ Mun (see [ ]). Abstract In this paper, a general theorem concerning absolute matrix summability is established by applying the concepts of almost increasing and δ-quasi-monotone sequences. A sequence (cn) is said to be δ-quasi-monotone, if cn → , cn > and cn ≥ –δn, where cn = cn – cn+ and δ = (δn) is a sequence of positive numbers (see [ ]).

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