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Journal of Function Spaces
Volume 2017, Article ID 1946394, 6 pages
https://doi.org/10.1155/2017/1946394
Research Article

Hyperstability of Some Functional Equations on Restricted Domain

Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland

Correspondence should be addressed to Anna Bahyrycz; moc.liamg@azcyryhab

Received 20 April 2017; Accepted 30 May 2017; Published 16 July 2017

Academic Editor: Adrian Petrusel

Copyright © 2017 Anna Bahyrycz and Jolanta Olko. 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.

Abstract

The paper concerns functions which approximately satisfy, not necessarily on the whole linear space, a generalization of linear functional equation. A Hyers-Ulam stability result is proved and next applied to give conditions implying the hyperstability of the equation. The results may be used as tools in stability studies on restricted domains for various functional equations. We use the main theorem to obtain a few hyperstability results of Fréchet equation on restricted domain for different control functions.