Proceedings of the 2015 International Conference on Intelligent Systems Research and Mechatronics Engineering

Estimation of unknown function of a class of retarded iterated integral inequalities

Authors
Jiting Huang, Wusheng Wang, Yun Ouyang, Yongzhou Qin
Corresponding Author
Jiting Huang
Available Online April 2015.
DOI
10.2991/isrme-15.2015.72How to use a DOI?
Keywords
integral inequality; unknown function; anlysis techniques; estimation
Abstract

It is well known that differential equations and integral equations are important tools to discuss the rule of natural phenomena. Various generalizations of the Gronwall-Bellman inequality are important tools in the study of existence, uniqueness, boundedness, stability, continuous dependence on the initial value and parameters, and other qualitative properties of solutions of differential equations and integral equation. In this paper, we discuss a class of retarded iterated integral inequalities, which includes a nonconstant term outside the integrals. By adopting novel analysis techniques, the upper bound of the embedded unknown function is estimated explicitly. The derived result can be applied in the study of solutions of ordinary differential equations and integral equations.

Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2015 International Conference on Intelligent Systems Research and Mechatronics Engineering
Series
Advances in Intelligent Systems Research
Publication Date
April 2015
ISBN
10.2991/isrme-15.2015.72
ISSN
1951-6851
DOI
10.2991/isrme-15.2015.72How to use a DOI?
Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Jiting Huang
AU  - Wusheng Wang
AU  - Yun Ouyang
AU  - Yongzhou Qin
PY  - 2015/04
DA  - 2015/04
TI  - Estimation of unknown function of a class of retarded iterated integral inequalities
BT  - Proceedings of the 2015 International Conference on Intelligent Systems Research and Mechatronics Engineering
PB  - Atlantis Press
SP  - 337
EP  - 342
SN  - 1951-6851
UR  - https://doi.org/10.2991/isrme-15.2015.72
DO  - 10.2991/isrme-15.2015.72
ID  - Huang2015/04
ER  -