Generalized Stability of a General Quartic Functional Equation
Sun-Sook Jin *
Department of Mathematics Education, Gongju National University of Education, Gongju 32553, Republic of Korea.
Yang-Hi Lee
Department of Mathematics Education, Gongju National University of Education, Gongju 32553, Republic of Korea.
*Author to whom correspondence should be addressed.
Abstract
The general quartic functional equation is a generalization of many functional equations such as a Jensen functional equation and a general quadratic functional equation. In this paper, we investigate the generalized stability of the general quartic functional equation $$\sum_{i=0}^{5}\dbinom{5}{i}(-1)^{5-i}f(x+iy)=0$$ using a direct method that modifies the proof method of Gavruta in Gavruta (1994).
Keywords: Stability of a functional equation, general quartic functional equation, general quartic mapping