Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions
Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6655630 |
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| _version_ | 1832546808873615360 |
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| author | Ömer Kişi |
| author_facet | Ömer Kişi |
| author_sort | Ömer Kişi |
| collection | DOAJ |
| description | Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α-level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions. |
| format | Article |
| id | doaj-art-672e5b8136cb4f9fab9d24a498e296cd |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-672e5b8136cb4f9fab9d24a498e296cd2025-02-03T06:47:03ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66556306655630Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued FunctionsÖmer Kişi0Faculty of Science, Department of Mathematics, Bartin University, Bartın, TurkeyBased on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α-level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.http://dx.doi.org/10.1155/2021/6655630 |
| spellingShingle | Ömer Kişi Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions Journal of Mathematics |
| title | Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions |
| title_full | Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions |
| title_fullStr | Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions |
| title_full_unstemmed | Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions |
| title_short | Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions |
| title_sort | lacunary statistical convergence in measure for double sequences of fuzzy valued functions |
| url | http://dx.doi.org/10.1155/2021/6655630 |
| work_keys_str_mv | AT omerkisi lacunarystatisticalconvergenceinmeasurefordoublesequencesoffuzzyvaluedfunctions |