Korean J. Math. Vol. 28 No. 2 (2020) pp.205-221
DOI: https://doi.org/10.11568/kjm.2020.28.2.205

A new paranormed series space using Euler totient means and some matrix transformations

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Published: Jun 30, 2020
Keywords:
Paranormed sequence spaces, Absolute summability, Euler Totient means, Matrix transformations
Mathematics Subject Classification:
40C05, 40F05, 46A45, 46A35, 46B50

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G. Canan Hazar Güleç
Department of Mathematics, Faculty of Science and Arts Pamukkale University, Denizli, Turkey.
Merve İlkhan
Department of Mathematics, Faculty of Science and Arts Duzce University, Duzce, Turkey.

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 $ \left\vert \phi _{z}\right\vert \left( p\right) $ over the paranormed space $ \ell \left( p\right) $ using Euler totient means, where $p=\left( p_{k}\right) $ is a bounded sequence of positive real numbers. Besides this, we investigate topological properties and compute the $ \alpha -,\beta -,$ and $\gamma $ duals of this paranormed space. Finally, we characterize the classes of infinite matrices $(\left\vert \phi_{z}\right\vert \left( p\right) ,\lambda )$ and $(\lambda ,\left\vert \phi_{z}\right\vert \left( p\right) ),$\ where $\lambda $ is any given sequence space.


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