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Journal of Inequalities and Applications
Published in: Journal of Inequalities and Applications 1/2006

Open Access 01-12-2006 | Research Article

Generalized orthogonal stability of some functional equations

Author: Justyna Sikorska

Published in: Journal of Inequalities and Applications | Issue 1/2006

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Abstract

We deal with a conditional functional inequality https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F12404/MediaObjects/13660_2005_Article_1566_IEq1_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F12404/MediaObjects/13660_2005_Article_1566_IEq2_HTML.gif is a given orthogonality relation, https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F12404/MediaObjects/13660_2005_Article_1566_IEq3_HTML.gif is a given nonnegative number, and https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F12404/MediaObjects/13660_2005_Article_1566_IEq4_HTML.gif is a given real number. Under suitable assumptions, we prove that any solution https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F12404/MediaObjects/13660_2005_Article_1566_IEq5_HTML.gif of the above inequality has to be uniformly close to an orthogonally additive mapping https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F12404/MediaObjects/13660_2005_Article_1566_IEq6_HTML.gif , that is, satisfying the condition https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F12404/MediaObjects/13660_2005_Article_1566_IEq7_HTML.gif . In the sequel, we deal with some other functional inequalities and we also present some applications and generalizations of the first result.
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Metadata
Title
Generalized orthogonal stability of some functional equations
Author
Justyna Sikorska
Publication date
01-12-2006
Publisher
Springer International Publishing
Published in
Journal of Inequalities and Applications / Issue 1/2006
Electronic ISSN: 1029-242X
DOI
https://doi.org/10.1155/JIA/2006/12404

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