Strong and weak convergences in 2-probabilistic normed spaces
In this paper, we have introduced the notions of strong and weak convergences in 2-probabilistic normed spaces (2-PN spaces) and established some of its properties. Later, we have defined the strong and weak boundedness of a linear map between two 2-PN spaces and proved a necessary and sufficient...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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ATNAA
2021-06-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1718882 |
| _version_ | 1797909617917820928 |
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| author | Panackal Harikrishnan Bernardo Lafuerza Guillen Ravi P. Agarwal Hamid Reza Moradi |
| author_facet | Panackal Harikrishnan Bernardo Lafuerza Guillen Ravi P. Agarwal Hamid Reza Moradi |
| author_sort | Panackal Harikrishnan |
| collection | DOAJ |
| description | In this paper, we have introduced the notions of strong and weak convergences in 2-probabilistic normed
spaces (2-PN spaces) and established some of its properties. Later, we have defined the strong and weak
boundedness of a linear map between two 2-PN spaces and proved a necessary and sufficient condition for
the linear map between two 2-PN spaces to be strongly and weakly bounded. |
| first_indexed | 2024-04-10T11:11:15Z |
| format | Article |
| id | doaj.art-73d04a2cf23a4ded9090bdaf56de557d |
| institution | Directory Open Access Journal |
| issn | 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T11:11:15Z |
| publishDate | 2021-06-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-73d04a2cf23a4ded9090bdaf56de557d2023-02-15T16:19:07ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482021-06-015445446610.31197/atnaa.921900Strong and weak convergences in 2-probabilistic normed spacesPanackal HarikrishnanBernardo Lafuerza GuillenRavi P. AgarwalHamid Reza MoradiIn this paper, we have introduced the notions of strong and weak convergences in 2-probabilistic normed spaces (2-PN spaces) and established some of its properties. Later, we have defined the strong and weak boundedness of a linear map between two 2-PN spaces and proved a necessary and sufficient condition for the linear map between two 2-PN spaces to be strongly and weakly bounded.https://dergipark.org.tr/tr/download/article-file/1718882menger's probabilistic normed spaceslinear 2-normed spacestriangle functionst-norms |
| spellingShingle | Panackal Harikrishnan Bernardo Lafuerza Guillen Ravi P. Agarwal Hamid Reza Moradi Strong and weak convergences in 2-probabilistic normed spaces Advances in the Theory of Nonlinear Analysis and its Applications menger's probabilistic normed spaces linear 2-normed spaces triangle functions t-norms |
| title | Strong and weak convergences in 2-probabilistic normed spaces |
| title_full | Strong and weak convergences in 2-probabilistic normed spaces |
| title_fullStr | Strong and weak convergences in 2-probabilistic normed spaces |
| title_full_unstemmed | Strong and weak convergences in 2-probabilistic normed spaces |
| title_short | Strong and weak convergences in 2-probabilistic normed spaces |
| title_sort | strong and weak convergences in 2 probabilistic normed spaces |
| topic | menger's probabilistic normed spaces linear 2-normed spaces triangle functions t-norms |
| url | https://dergipark.org.tr/tr/download/article-file/1718882 |
| work_keys_str_mv | AT panackalharikrishnan strongandweakconvergencesin2probabilisticnormedspaces AT bernardolafuerzaguillen strongandweakconvergencesin2probabilisticnormedspaces AT ravipagarwal strongandweakconvergencesin2probabilisticnormedspaces AT hamidrezamoradi strongandweakconvergencesin2probabilisticnormedspaces |