On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces
An ideal I is a hereditary and additive family of subsets of positive integers ℕ. In this paper, we will introduce the concept of generalized random n-normed space as an extension of random n-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence and L-ideal Cauchy for seque...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/101782 |
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| author | Awad A. Bakery Mustafa M. Mohammed |
| author_facet | Awad A. Bakery Mustafa M. Mohammed |
| author_sort | Awad A. Bakery |
| collection | DOAJ |
| description | An ideal I is a hereditary and additive family of subsets of positive integers ℕ. In this paper, we will introduce the concept of generalized random n-normed space as an extension of random n-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence and L-ideal Cauchy for sequences of complex numbers in the generalized random n-norm. We introduce IL-limit points and IL-cluster points. Furthermore, Cauchy and IL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts. |
| format | Article |
| id | doaj-art-46dbb7dc5a7f488f8198d7365d89f198 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-46dbb7dc5a7f488f8198d7365d89f1982025-02-03T05:48:22ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/101782101782On Lacunary Mean Ideal Convergence in Generalized Random n-Normed SpacesAwad A. Bakery0Mustafa M. Mohammed1Department of Mathematics, Faculty of Science and Arts, King Abdulaziz University (KAU), P.O. Box 80200, Khulais 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science and Arts, King Abdulaziz University (KAU), P.O. Box 80200, Khulais 21589, Saudi ArabiaAn ideal I is a hereditary and additive family of subsets of positive integers ℕ. In this paper, we will introduce the concept of generalized random n-normed space as an extension of random n-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence and L-ideal Cauchy for sequences of complex numbers in the generalized random n-norm. We introduce IL-limit points and IL-cluster points. Furthermore, Cauchy and IL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.http://dx.doi.org/10.1155/2014/101782 |
| spellingShingle | Awad A. Bakery Mustafa M. Mohammed On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces Abstract and Applied Analysis |
| title | On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces |
| title_full | On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces |
| title_fullStr | On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces |
| title_full_unstemmed | On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces |
| title_short | On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces |
| title_sort | on lacunary mean ideal convergence in generalized random n normed spaces |
| url | http://dx.doi.org/10.1155/2014/101782 |
| work_keys_str_mv | AT awadabakery onlacunarymeanidealconvergenceingeneralizedrandomnnormedspaces AT mustafammohammed onlacunarymeanidealconvergenceingeneralizedrandomnnormedspaces |