On I θ 2 $\mathcal{I}_{{\theta}_{2}}$ -convergence in fuzzy normed spaces
Abstract In this study, first, lacunary convergence of double sequences is introduced in fuzzy normed spaces, and basic definitions and theorems about lacunary convergence for double sequences are given in fuzzy normed spaces. Then, we introduce the concept of lacunary ideal convergence of double se...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-05-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-020-02387-9 |
| _version_ | 1819103744775684096 |
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| author | Muhammed Recai Türkmen |
| author_facet | Muhammed Recai Türkmen |
| author_sort | Muhammed Recai Türkmen |
| collection | DOAJ |
| description | Abstract In this study, first, lacunary convergence of double sequences is introduced in fuzzy normed spaces, and basic definitions and theorems about lacunary convergence for double sequences are given in fuzzy normed spaces. Then, we introduce the concept of lacunary ideal convergence of double sequences in fuzzy normed spaces, and the relation between lacunary convergence and lacunary ideal convergence is investigated for double sequences in fuzzy normed spaces. Finally, in fuzzy normed spaces, we give the concept of limit point and cluster point for double sequences, and the theorems related to these concepts are given. |
| first_indexed | 2024-12-22T01:55:20Z |
| format | Article |
| id | doaj.art-2c920eac661842378c6534f4b411b817 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-22T01:55:20Z |
| publishDate | 2020-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-2c920eac661842378c6534f4b411b8172022-12-21T18:42:49ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-05-012020111110.1186/s13660-020-02387-9On I θ 2 $\mathcal{I}_{{\theta}_{2}}$ -convergence in fuzzy normed spacesMuhammed Recai Türkmen0Deparment of Mathematics and Science Education, Faculty of Education, Afyon Kocatepe UniversityAbstract In this study, first, lacunary convergence of double sequences is introduced in fuzzy normed spaces, and basic definitions and theorems about lacunary convergence for double sequences are given in fuzzy normed spaces. Then, we introduce the concept of lacunary ideal convergence of double sequences in fuzzy normed spaces, and the relation between lacunary convergence and lacunary ideal convergence is investigated for double sequences in fuzzy normed spaces. Finally, in fuzzy normed spaces, we give the concept of limit point and cluster point for double sequences, and the theorems related to these concepts are given.http://link.springer.com/article/10.1186/s13660-020-02387-9Statistical convergenceFuzzy normed spacesLacunary convergenceI $\mathcal{I}$ -convergenceDouble sequence |
| spellingShingle | Muhammed Recai Türkmen On I θ 2 $\mathcal{I}_{{\theta}_{2}}$ -convergence in fuzzy normed spaces Journal of Inequalities and Applications Statistical convergence Fuzzy normed spaces Lacunary convergence I $\mathcal{I}$ -convergence Double sequence |
| title | On I θ 2 $\mathcal{I}_{{\theta}_{2}}$ -convergence in fuzzy normed spaces |
| title_full | On I θ 2 $\mathcal{I}_{{\theta}_{2}}$ -convergence in fuzzy normed spaces |
| title_fullStr | On I θ 2 $\mathcal{I}_{{\theta}_{2}}$ -convergence in fuzzy normed spaces |
| title_full_unstemmed | On I θ 2 $\mathcal{I}_{{\theta}_{2}}$ -convergence in fuzzy normed spaces |
| title_short | On I θ 2 $\mathcal{I}_{{\theta}_{2}}$ -convergence in fuzzy normed spaces |
| title_sort | on i θ 2 mathcal i theta 2 convergence in fuzzy normed spaces |
| topic | Statistical convergence Fuzzy normed spaces Lacunary convergence I $\mathcal{I}$ -convergence Double sequence |
| url | http://link.springer.com/article/10.1186/s13660-020-02387-9 |
| work_keys_str_mv | AT muhammedrecaiturkmen onith2mathcalitheta2convergenceinfuzzynormedspaces |