Open Access

On Stability of a Functional Equation Connected with the Reynolds Operator

Journal of Inequalities and Applications20072007:079816

DOI: 10.1155/2007/79816

Received: 18 July 2006

Accepted: 3 December 2006

Published: 14 January 2007

Abstract

Let https://static-content.springer.com/image/art%3A10.1155%2F2007%2F79816/MediaObjects/13660_2006_Article_1741_IEq1_HTML.gif be an Abelain semigroup, https://static-content.springer.com/image/art%3A10.1155%2F2007%2F79816/MediaObjects/13660_2006_Article_1741_IEq2_HTML.gif , and let https://static-content.springer.com/image/art%3A10.1155%2F2007%2F79816/MediaObjects/13660_2006_Article_1741_IEq3_HTML.gif be either https://static-content.springer.com/image/art%3A10.1155%2F2007%2F79816/MediaObjects/13660_2006_Article_1741_IEq4_HTML.gif or https://static-content.springer.com/image/art%3A10.1155%2F2007%2F79816/MediaObjects/13660_2006_Article_1741_IEq5_HTML.gif . We prove superstability of the functional equation https://static-content.springer.com/image/art%3A10.1155%2F2007%2F79816/MediaObjects/13660_2006_Article_1741_IEq6_HTML.gif in the class of functions https://static-content.springer.com/image/art%3A10.1155%2F2007%2F79816/MediaObjects/13660_2006_Article_1741_IEq7_HTML.gif . We also show some stability results of the equation in the class of functions https://static-content.springer.com/image/art%3A10.1155%2F2007%2F79816/MediaObjects/13660_2006_Article_1741_IEq8_HTML.gif .

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Authors’ Affiliations

(1)
Institute of Mathematics, University of Rzeszów

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Copyright

© Adam Najdecki 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.