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Generalized orthogonal stability of some functional equations

Journal of Inequalities and Applications volume 2006, Article number: 12404 (2006) Cite this article

Abstract

We deal with a conditional functional inequality, where is a given orthogonality relation, is a given nonnegative number, and is a given real number. Under suitable assumptions, we prove that any solution of the above inequality has to be uniformly close to an orthogonally additive mapping, that is, satisfying the condition. 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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  1. Institute of Mathematics, University of Silesian, Bankowa 14, Katowice, 40-007, Poland

    Justyna Sikorska

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  1. Justyna Sikorska
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Correspondence to Justyna Sikorska.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sikorska, J. Generalized orthogonal stability of some functional equations. J Inequal Appl 2006, 12404 (2006). https://doi.org/10.1155/JIA/2006/12404

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