On paranormed sequence space arising from Riesz Euler Totient matrix

Pınar Zengin Alp; Pınar Zengin Alp

doi:10.3934/math.2025510

AIMS Mathematics

2025, Volume 10, Issue 5: 11260-11270. doi: 10.3934/math.2025510

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On paranormed sequence space arising from Riesz Euler Totient matrix

Pınar Zengin Alp ^,

Department of Mathematics, Duzce University, Duzce, Turkey

Received: 30 December 2024 Revised: 28 April 2025 Accepted: 06 May 2025 Published: 19 May 2025
MSC : 46B45, 47B06, 47H08

In this paper, we introduce a novel paranormed sequence space $ \mathit{l} ({R_{\Phi}}, p) $ constructed through the application of the Riesz Euler Totient matrix. We demonstrate that the spaces $ \mathit{l} ({R_{\Phi}}, p) $ and $ \mathit{l} (p) $ are linearly isomorphic. In addition, we identify the dual spaces associated with this sequence space and establish its Schauder basis.
- $ \alpha $-, $ \beta $-, $ \gamma $-duals,
- paranormed sequence space,
- Riesz matrix,
- Euler Totient function
Citation: Pınar Zengin Alp. On paranormed sequence space arising from Riesz Euler Totient matrix[J]. AIMS Mathematics, 2025, 10(5): 11260-11270. doi: 10.3934/math.2025510

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Abstract

In this paper, we introduce a novel paranormed sequence space $ \mathit{l} ({R_{\Phi}}, p) $ constructed through the application of the Riesz Euler Totient matrix. We demonstrate that the spaces $ \mathit{l} ({R_{\Phi}}, p) $ and $ \mathit{l} (p) $ are linearly isomorphic. In addition, we identify the dual spaces associated with this sequence space and establish its Schauder basis.

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