- Mathematical Sciences and Applications E-Notes
- Volume:8 Issue:1
- A New Paranormed Series Space and Matrix Transformations
A New Paranormed Series Space and Matrix Transformations
Authors : G Canan HAZAR GÜLEÇ
Pages : 91-99
Doi:10.36753/mathenot.627066
View : 52 | Download : 7
Publication Date : 2020-03-20
Article Type : Research Paper
Abstract :Recently, Hazar and Sarıgöl have defined and studied the series space |C₋₁|_{p} for 1≤p<∞ in [1]. The aim of this study is to introduce a new paranormed space |C₋₁|insert ignore into journalissuearticles values(p);, where p=insert ignore into journalissuearticles values(p_{k}); is a bounded sequence of positive real numbers, which extends the results of Hazar and Sarıgöl in [1] to paranormed space. Besides this, we investigate topological properties and compute the α-,β-, and γ duals of this paranormed space. Finally, we characterize the classes of infinite matrices insert ignore into journalissuearticles values(|C₋₁|insert ignore into journalissuearticles values(p);,μ); and insert ignore into journalissuearticles values(μ,|C₋₁|insert ignore into journalissuearticles values(p););, where μ is any given sequence spacesKeywords : Paranormed sequence spaces, Absolute summability, Cesàro means, Matrix transformations
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