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

G. Canan Hazar Güleç, Merve İlkhan


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.


Paranormed sequence spaces, Absolute summability, Euler Totient means; Matrix transformations

Subject classification

40C05, 40F05, 46A45, 46A35, 46B50


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