On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz Functions
In this article we have introduced the sequence space $m(\phi,d)$ and $m(M,\phi,d)$ of W. L. C. Sargent type in a metric space $(X, d)$ on generalising the sequence space $m(\phi)$ and we have defined these sequence spaces using the Orlicz function $M$. We have investigated their different propertie...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2022-10-01
|
| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_255058_e77af399e2a00cd50168319a19d9b941.pdf |
| _version_ | 1811180275896418304 |
|---|---|
| author | Rinku Dey Binod Tripathy |
| author_facet | Rinku Dey Binod Tripathy |
| author_sort | Rinku Dey |
| collection | DOAJ |
| description | In this article we have introduced the sequence space $m(\phi,d)$ and $m(M,\phi,d)$ of W. L. C. Sargent type in a metric space $(X, d)$ on generalising the sequence space $m(\phi)$ and we have defined these sequence spaces using the Orlicz function $M$. We have investigated their different properties like solidness, symmetricity, monotone, sequence algebra, completeness etc. We have established some inclusion results involving the space $m(M,\phi,d)$ and some of the existing sequence spaces. We have provided suitable examples and discussed in detail, in order to justify the failure cases and the definitions we have introduced. The results established in this article generalized and unifies several existing results. |
| first_indexed | 2024-04-11T06:48:39Z |
| format | Article |
| id | doaj.art-04543d79a6614f69ac06fe4cd5413d8f |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-04-11T06:48:39Z |
| publishDate | 2022-10-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-04543d79a6614f69ac06fe4cd5413d8f2022-12-22T04:39:17ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002022-10-01194253810.22130/scma.2022.538729.986255058On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz FunctionsRinku Dey0Binod Tripathy1Department of Mathematics, Jagannath Barooah College, Jorhat 785001, Assam, India.Department of Mathematics, Tripura University, Suryamaninagar, Agartala799022, Tripura, India.In this article we have introduced the sequence space $m(\phi,d)$ and $m(M,\phi,d)$ of W. L. C. Sargent type in a metric space $(X, d)$ on generalising the sequence space $m(\phi)$ and we have defined these sequence spaces using the Orlicz function $M$. We have investigated their different properties like solidness, symmetricity, monotone, sequence algebra, completeness etc. We have established some inclusion results involving the space $m(M,\phi,d)$ and some of the existing sequence spaces. We have provided suitable examples and discussed in detail, in order to justify the failure cases and the definitions we have introduced. The results established in this article generalized and unifies several existing results.https://scma.maragheh.ac.ir/article_255058_e77af399e2a00cd50168319a19d9b941.pdfmetric spaceorlicz function$p$-absolutely summable sequencessolid spacesymmetric space |
| spellingShingle | Rinku Dey Binod Tripathy On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz Functions Sahand Communications in Mathematical Analysis metric space orlicz function $p$-absolutely summable sequences solid space symmetric space |
| title | On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz Functions |
| title_full | On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz Functions |
| title_fullStr | On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz Functions |
| title_full_unstemmed | On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz Functions |
| title_short | On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz Functions |
| title_sort | on a class of sequences related to p absolutely summable sequences in metric space defined by orlicz functions |
| topic | metric space orlicz function $p$-absolutely summable sequences solid space symmetric space |
| url | https://scma.maragheh.ac.ir/article_255058_e77af399e2a00cd50168319a19d9b941.pdf |
| work_keys_str_mv | AT rinkudey onaclassofsequencesrelatedtopabsolutelysummablesequencesinmetricspacedefinedbyorliczfunctions AT binodtripathy onaclassofsequencesrelatedtopabsolutelysummablesequencesinmetricspacedefinedbyorliczfunctions |