Generalized vector-valued paranormed sequence space using modulus function

摘要

In this paper we introduce a generalized vector-valued paranormed sequence space Np(Ek,Δm,f,s) using modulus function f, where p=(pk) is a bounded sequence of positive real numbers such that infkpk>0,(Ek,qk) is a sequence of seminormed spaces with Ek+1⊆Ek for each k ∈ N and s⩾0. We have also studied sequence space Np(Ek,Δm,fr,s), where fr=f∘f∘f∘,…,f (r-times composition of f with itself) and r∈N={1,2,3,…}. Results regarding completeness, K-space, normality, inclusion relations etc. are derived. Further, a study of multiplier of the set Np(Ek,f,s) is also made by choosing (Ek,‖·‖k) as sequence of normed algebras.