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Generalized vector-valued paranormed sequence space using modulus function
Authors:P.D. Srivastava  Sudhanshu Kumar
Affiliation:Department of Mathematics, Indian Institute of Technology, Kharagpur, Kharagpur 721 302, India
Abstract:In this paper we introduce a generalized vector-valued paranormed sequence space Np(Ekm,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+1Ek for each kN and s?0. We have also studied sequence space Np(Ekm,fr,s), where fr=f°f°f°,…,f (r-times composition of f with itself) and rN={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.
Keywords:Modulus function   Paranormed space   Normal sequence space   Difference sequence space
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