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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a Stieltjes version of Gronwall's inequality


Author: Angelo B. Mingarelli
Journal: Proc. Amer. Math. Soc. 82 (1981), 249-252
MSC: Primary 34A40
DOI: https://doi.org/10.1090/S0002-9939-1981-0609660-1
MathSciNet review: 609660
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Abstract: A unified formulation of Gronwall's inequality $ ({\text{GI}})$ for certain Stieltjes integrals is presented. An advantage in using Stieltjes integrals lies in the fact that some of the "continuous" and "discrete" versions of the inequality may be obtained as a consequence of the same theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0609660-1
Keywords: Gronwall inequality, Riemann-Stieltjes integral, Cauchy-Stieltjes integral, mean Stieltjes integral, interior integral
Article copyright: © Copyright 1981 American Mathematical Society