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http://dx.doi.org/10.11568/kjm.2020.28.2.205

A NEW PARANORMED SERIES SPACE USING EULER TOTIENT MEANS AND SOME MATRIX TRANSFORMATIONS  

Gulec, G. Canan Hazar (Department of Mathematics, Faculty of Science and Arts Pamukkale University)
Ilkhan, Merve (Department of Mathematics, Faculty of Science and Arts Duzce University)
Publication Information
Korean Journal of Mathematics / v.28, no.2, 2020 , pp. 205-221 More about this Journal
Abstract
Paranormed spaces are important as a generalization of the normed spaces in terms of having more general properties. The aim of this study is to introduce a new paranormed space |𝜙z|(p) over the paranormed space ℓ(p) using Euler totient means, where p = (pk) is a bounded sequence of positive real numbers. 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 (|𝜙z|(p), λ) and (λ, |𝜙z|(p)), where λ is any given sequence space.
Keywords
Paranormed sequence spaces; Absolute summability; Euler totient means; Matrix transformations;
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