A new generalized class of difference sequence spaces defined by Orlicz function

Nilambar Tripathy; Ramakant  Rath

doi:10.5269/bspm.68337

Nilambar Tripathy IIIT, Bhubaneswar
Ramakant Rath Kamala Nehru Women's College, Bhubaneswar

Résumé

In this article, our aim is to introduce a new generalized class of vector valued sequence space $F(E_k, \Delta^m_\nu, M,p,q)$ using Orlicz function $M$, where $(E_k)_{k=1}^{\infty}$ is the class of all seminormed space ~$(E_k,q_k)$ ~with $E_{k+1}\subseteq E_k$. It is assumed that $F$ is a normal, $AK$-sequence space with absolutely monotone paranorm $g_F$ and $p=(p_k)$ is a bounded sequence of positive real numbers. Here it is also proved that the space is a complete paranormed space under the paranorm $g$ along with cetrain inclusion relations.

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