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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 973586, 8 pages
Research Article

On Some Vector-Valued Inequalities of Gronwall Type

Department of Applied Mathematics, I-Shou University, No. 1, Sec. 1, Syuecheng Road, Dashu District, Kaohsiung City 84001, Taiwan

Received 25 October 2013; Accepted 12 December 2013; Published 22 January 2014

Academic Editor: Weinian Zhang

Copyright © 2014 Dah-Chin Luor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.