Article
Kyungpook Mathematical Journal 2018; 58(2): 291-305
Published online June 23, 2018
Copyright © Kyungpook Mathematical Journal.
A General Uniqueness Theorem concerning the Stability of AQCQ Type Functional Equations
Yang-Hi Lee and Soon-Mo Jung*
Department of Mathematics Education, Gongju National University of Education, 32553 Gongju, Republic of Korea, e-mail : yanghi2@hanmail.net, Mathematics Section, College of Science and Technology, Hongik University, 30016 Sejong, Republic of Korea, e-mail: smjung@hongik.ac.kr
Received: August 24, 2017; Accepted: April 12, 2018
In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.
Keywords: uniqueness, stability, Hyers-Ulam stability, generalized Hyers-Ulam stability, AQCQ type functional equation, AQCQ mapping