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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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참고문헌 (33)
참고문헌 신청
B. Altay / 2003 / On the paranormed Riesz sequence spaces of non-absolute type / Southeast Asian Bull. Math 26(5):701~715
B. Altay / 2007 / Generalization of the sequence spaces ℓ(p)derived by weighted mean / J. Math. Anal. Appl 330:174~185
B. Altay / 2006 / On the Euler sequence spaces which include the spaces ℓ(p)and ℓ∞ I / Inform. Sci 176(10):1450~1462
C. Aydın / 2005 / Some new sequence spaces which incule the spaces ℓp and ℓ∞ / Demonstratio Math 38(3):641~656
C. Aydın / 2006 / Some generalizations of the sequence space, Iran / J. Sci. Technol. Trans. A Sci. 30(A2):175~190
B. Altay / 2007 / Generalization of the sequence spaces ℓ(p)derived by weighted mean / J. Math. Anal. Appl 330:174~185
B. Altay / 2006 / On the Euler sequence spaces which include the spaces ℓ(p)and ℓ∞ I / Inform. Sci 176(10):1450~1462
C. Aydın / 2005 / Some new sequence spaces which incule the spaces ℓp and ℓ∞ / Demonstratio Math 38(3):641~656
C. Aydın / 2006 / Some generalizations of the sequence space, Iran / J. Sci. Technol. Trans. A Sci. 30(A2):175~190
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