Generalized vector-valued paranormed sequence spaces defined by a sequence of Orlicz functions
UDC 517.9 We introduced a class of generalized vector-valued paranormed sequence space $X[E,A,\Delta_v^m,M,p]$ by using a sequence of Orlicz functions $M=(M_k),$ a non-negative infinite matrix $A=[a_{nk}],$ generalized difference operator $\Delta_v^m$ and bounded sequence of positive real numbers $p...
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| Date: | 2022 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6549 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.9
We introduced a class of generalized vector-valued paranormed sequence space $X[E,A,\Delta_v^m,M,p]$ by using a sequence of Orlicz functions $M=(M_k),$ a non-negative infinite matrix $A=[a_{nk}],$ generalized difference operator $\Delta_v^m$ and bounded sequence of positive real numbers $p_k$ with $\inf_k p_k>0.$ Properties related to this space are studied under certain conditions. Some inclusion relations are obtained and a result related to subspace with Orlicz functions satisfying $\Delta_2$-condition has also been proved. |
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| DOI: | 10.37863/umzh.v74i4.6549 |