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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 16, Issue 7 (Jan 2008)


Unimprovable estimates of solutions for some classes of integral inequalities

A. S. Apartsyn
Published Online: 2008-11-21 | DOI: https://doi.org/10.1515/JIIP.2008.040


In this paper the method of obtaining unimprovable (in certain sense) estimates of solutions of some integral inequalities with the operators of Volterra type is stated. The basis of this method is the theory of monotone operators in partially ordered Banach spaces. This theory allows us to reduce obtaining these estimates to solving corresponding equations. The paper consists of two parts. The first part is devoted to unimprovable estimates of solutions for linear multidimensional inequalities. In the second part the author states nonlinear inequalities which arise while researching multilinear Volterra equations of the first kind connected with modelling nonlinear dynamic systems of black body type by Volterra polynomials.

Key words.: Unimprovable estimates; linear multidimensional and nonlinear one-dimensional Volterra integral inequalities

About the article

Received: 2008-03-17

Published Online: 2008-11-21

Published in Print: 2008-11-01

Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2008.040. Export Citation

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