On sequence ideal using Orlicz function and de la Vallée Poussin mean

Abstract

In this paper we have introduced a new sequence ideal using Orlicz function and the notion of de la Vallée Poussin mean. It is proved that the Cesáro-Orlicz sequence ideal is complete under a suitable norm. Moreover, it is shown that Cesáro-Orlicz sequence ideal is maximal, and if the Orlicz function satisfies Δ2-condition at zero then it is also minimal.

Keywords

• Sequence ideals
• Orlicz function
• de la Vallée Poussin mean