Soft Limit and Soft Continuity
This study presents the soft limit and upper (lower) soft limit proposed by Molodtsov, with several theoretical contributions. It investigates some of their basic properties, such as some fundamental soft limit rules, the relation between soft limit and boundedness, and the sandwich/squeeze theorem....
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-05-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/5/2/65 |
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| author | Kenan Sapan Burak Arslan Serdar Enginoğlu |
| author_facet | Kenan Sapan Burak Arslan Serdar Enginoğlu |
| author_sort | Kenan Sapan |
| collection | DOAJ |
| description | This study presents the soft limit and upper (lower) soft limit proposed by Molodtsov, with several theoretical contributions. It investigates some of their basic properties, such as some fundamental soft limit rules, the relation between soft limit and boundedness, and the sandwich/squeeze theorem. Moreover, the paper proposes left and right soft limits and studies some of their main properties. Furthermore, it defines the soft limit at infinity and explores some of its basic properties. Additionally, the present study exemplifies these concepts and their properties to better understand them. The paper then compares the aforesaid concepts with their classical forms. Afterward, this paper presents soft continuity and upper (lower) soft continuity, proposed by Molodtsov, theoretically contributes to these concepts, and investigates some of their key properties, such as some fundamental soft continuity rules, the relation between soft continuity and boundedness, Bolzano’s theorem, and the intermediate value theorem. Moreover, it defines left and right soft continuity and studies some of their basic properties. The present study exemplifies soft continuity types and their properties. In addition, it compares them with their classical forms. Finally, this study discusses whether the aspects should be further analyzed. |
| format | Article |
| id | doaj-art-c54dec8ea7b9485b8d25b5d528d00e2a |
| institution | Kabale University |
| issn | 2673-9909 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj-art-c54dec8ea7b9485b8d25b5d528d00e2a2025-08-20T03:26:20ZengMDPI AGAppliedMath2673-99092025-05-01526510.3390/appliedmath5020065Soft Limit and Soft ContinuityKenan Sapan0Burak Arslan1Serdar Enginoğlu2Department of Mathematics, Faculty of Science, Çanakkale Onsekiz Mart University, Çanakkale 17020, TürkiyeDepartment of Mathematics, Faculty of Science, Çanakkale Onsekiz Mart University, Çanakkale 17020, TürkiyeDepartment of Mathematics, Faculty of Science, Çanakkale Onsekiz Mart University, Çanakkale 17020, TürkiyeThis study presents the soft limit and upper (lower) soft limit proposed by Molodtsov, with several theoretical contributions. It investigates some of their basic properties, such as some fundamental soft limit rules, the relation between soft limit and boundedness, and the sandwich/squeeze theorem. Moreover, the paper proposes left and right soft limits and studies some of their main properties. Furthermore, it defines the soft limit at infinity and explores some of its basic properties. Additionally, the present study exemplifies these concepts and their properties to better understand them. The paper then compares the aforesaid concepts with their classical forms. Afterward, this paper presents soft continuity and upper (lower) soft continuity, proposed by Molodtsov, theoretically contributes to these concepts, and investigates some of their key properties, such as some fundamental soft continuity rules, the relation between soft continuity and boundedness, Bolzano’s theorem, and the intermediate value theorem. Moreover, it defines left and right soft continuity and studies some of their basic properties. The present study exemplifies soft continuity types and their properties. In addition, it compares them with their classical forms. Finally, this study discusses whether the aspects should be further analyzed.https://www.mdpi.com/2673-9909/5/2/65soft setssoft analysissoft limitsoft continuity |
| spellingShingle | Kenan Sapan Burak Arslan Serdar Enginoğlu Soft Limit and Soft Continuity AppliedMath soft sets soft analysis soft limit soft continuity |
| title | Soft Limit and Soft Continuity |
| title_full | Soft Limit and Soft Continuity |
| title_fullStr | Soft Limit and Soft Continuity |
| title_full_unstemmed | Soft Limit and Soft Continuity |
| title_short | Soft Limit and Soft Continuity |
| title_sort | soft limit and soft continuity |
| topic | soft sets soft analysis soft limit soft continuity |
| url | https://www.mdpi.com/2673-9909/5/2/65 |
| work_keys_str_mv | AT kenansapan softlimitandsoftcontinuity AT burakarslan softlimitandsoftcontinuity AT serdarenginoglu softlimitandsoftcontinuity |