On Some Vector-Valued Inequalities of Gronwall Type
In this paper we established some vector-valued inequalities of Gronwall type in ordered Banach spaces. Our results can be applied to investigate systems of real-valued Gronwall-type inequalities. We also show that the classical Gronwall-Bellman-Bihari integral inequality can be generalized from com...
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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/10.1155/2014/973586 |
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| _version_ | 1832548415344476160 |
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| author | Dah-Chin Luor |
| author_facet | Dah-Chin Luor |
| author_sort | Dah-Chin Luor |
| collection | DOAJ |
| description | In this paper we established some vector-valued inequalities of Gronwall type in ordered Banach spaces. Our results can be applied to investigate systems of real-valued Gronwall-type inequalities. We also show that the classical Gronwall-Bellman-Bihari integral inequality can be generalized from composition operators to a variety of operators, which include integral operators, maximal operators, geometric mean operators, and geometric maximal operators. |
| format | Article |
| id | doaj-art-9cc6c11f633e460c99d493059ebe333f |
| 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-9cc6c11f633e460c99d493059ebe333f2025-02-03T06:14:09ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/973586973586On Some Vector-Valued Inequalities of Gronwall TypeDah-Chin Luor0Department of Applied Mathematics, I-Shou University, No. 1, Sec. 1, Syuecheng Road, Dashu District, Kaohsiung City 84001, TaiwanIn this paper we established some vector-valued inequalities of Gronwall type in ordered Banach spaces. Our results can be applied to investigate systems of real-valued Gronwall-type inequalities. We also show that the classical Gronwall-Bellman-Bihari integral inequality can be generalized from composition operators to a variety of operators, which include integral operators, maximal operators, geometric mean operators, and geometric maximal operators.http://dx.doi.org/10.1155/2014/973586 |
| spellingShingle | Dah-Chin Luor On Some Vector-Valued Inequalities of Gronwall Type Abstract and Applied Analysis |
| title | On Some Vector-Valued Inequalities of Gronwall Type |
| title_full | On Some Vector-Valued Inequalities of Gronwall Type |
| title_fullStr | On Some Vector-Valued Inequalities of Gronwall Type |
| title_full_unstemmed | On Some Vector-Valued Inequalities of Gronwall Type |
| title_short | On Some Vector-Valued Inequalities of Gronwall Type |
| title_sort | on some vector valued inequalities of gronwall type |
| url | http://dx.doi.org/10.1155/2014/973586 |
| work_keys_str_mv | AT dahchinluor onsomevectorvaluedinequalitiesofgronwalltype |