On Some Vector-Valued Inequalities of Gronwall Type

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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Main Author: Dah-Chin Luor
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/973586
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spelling doaj-9cc6c11f633e460c99d493059ebe333f2020-11-24T23:19:46ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Dah-Chin Luor
spellingShingle Dah-Chin Luor
On Some Vector-Valued Inequalities of Gronwall Type
Abstract and Applied Analysis
author_facet Dah-Chin Luor
author_sort Dah-Chin Luor
title On Some Vector-Valued Inequalities of Gronwall Type
title_short 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_sort on some vector-valued inequalities of gronwall type
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
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.
url http://dx.doi.org/10.1155/2014/973586
work_keys_str_mv AT dahchinluor onsomevectorvaluedinequalitiesofgronwalltype
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