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Journal of Function Spaces
Volume 2015 (2015), Article ID 643969, 8 pages
http://dx.doi.org/10.1155/2015/643969
Research Article

A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations

1Department of Mathematics Education, Gongju National University of Education, Gongju 314-711, Republic of Korea
2Mathematics Section, College of Science and Technology, Hongik University, Sejong 339-701, Republic of Korea

Received 16 October 2014; Accepted 20 January 2015

Academic Editor: Alberto Fiorenza

Copyright © 2015 Yang-Hi Lee and Soon-Mo Jung. 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

We prove a general uniqueness theorem that can be easily applied to the (generalized) Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadratic-additive type functional equations. This uniqueness theorem can replace the repeated proofs for uniqueness of the relevant solutions of given equations while we investigate the stability of functional equations.