Generalized Difference Lacunary Weak Convergence of Sequences
In this paper, we introduce the concept of generalized difference lacunary weak convergence of sequences. Using the concept of difference operator, we have introduced some new classes of sequences. We investigated several of its algebraic and topological properties, such as solidness, symmetry and m...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2024-03-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_709285_8d2e35d908ffef6b7eb09c7d76c1083d.pdf |
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| _version_ | 1823859413868347392 |
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| author | Bibhajyoti Tamuli Binod Tripathy |
| author_facet | Bibhajyoti Tamuli Binod Tripathy |
| author_sort | Bibhajyoti Tamuli |
| collection | DOAJ |
| description | In this paper, we introduce the concept of generalized difference lacunary weak convergence of sequences. Using the concept of difference operator, we have introduced some new classes of sequences. We investigated several of its algebraic and topological properties, such as solidness, symmetry and monotone. We gave appropriate examples and detailed discussions to validate our established failure instances and definitions. Further, we have established some inclusion relations of the introduced sequence spaces with other sequence spaces, in particularly with the weak Ces`aro summable sequences. |
| format | Article |
| id | doaj-art-98fd94a34d4544248cf7888e4166eb11 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-98fd94a34d4544248cf7888e4166eb112025-02-11T05:24:46ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-03-0121219520610.22130/scma.2023.2006321.1371709285Generalized Difference Lacunary Weak Convergence of SequencesBibhajyoti Tamuli0Binod Tripathy1Department of Mathematics, Tripura University, Suryamaninagar, Agartala 799022, India.Department of Mathematics, Tripura University, Suryamaninagar, Agartala 799022, India.In this paper, we introduce the concept of generalized difference lacunary weak convergence of sequences. Using the concept of difference operator, we have introduced some new classes of sequences. We investigated several of its algebraic and topological properties, such as solidness, symmetry and monotone. We gave appropriate examples and detailed discussions to validate our established failure instances and definitions. Further, we have established some inclusion relations of the introduced sequence spaces with other sequence spaces, in particularly with the weak Ces`aro summable sequences.https://scma.maragheh.ac.ir/article_709285_8d2e35d908ffef6b7eb09c7d76c1083d.pdflacunary sequenceweak convergenceces`aro summable sequencebanach spacesolid spacesymmetric space |
| spellingShingle | Bibhajyoti Tamuli Binod Tripathy Generalized Difference Lacunary Weak Convergence of Sequences Sahand Communications in Mathematical Analysis lacunary sequence weak convergence ces`aro summable sequence banach space solid space symmetric space |
| title | Generalized Difference Lacunary Weak Convergence of Sequences |
| title_full | Generalized Difference Lacunary Weak Convergence of Sequences |
| title_fullStr | Generalized Difference Lacunary Weak Convergence of Sequences |
| title_full_unstemmed | Generalized Difference Lacunary Weak Convergence of Sequences |
| title_short | Generalized Difference Lacunary Weak Convergence of Sequences |
| title_sort | generalized difference lacunary weak convergence of sequences |
| topic | lacunary sequence weak convergence ces`aro summable sequence banach space solid space symmetric space |
| url | https://scma.maragheh.ac.ir/article_709285_8d2e35d908ffef6b7eb09c7d76c1083d.pdf |
| work_keys_str_mv | AT bibhajyotitamuli generalizeddifferencelacunaryweakconvergenceofsequences AT binodtripathy generalizeddifferencelacunaryweakconvergenceofsequences |