A new generalized class of difference sequence spaces defined by Orlicz function
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.
Authors
- N. Tripathy
- Rabindra Narayan Mahapatra (ORCID: https://orcid.org/0009-0001-4655-870X)
Publication Details
- Journal
- Boletim da Sociedade Paranaense de Matemática
- Published
- 2025-03-24
- DOI
- https://doi.org/10.5269/bspm.68337
- Primary Topic
- Approximation Theory and Sequence Spaces
- Type
- article
- Field-Weighted Citation Impact
- 0.00