Hyers-Ulam-Rassias Stability of a General Septic 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
In this paper, we investigate the stability of the following general septic functional equation:
\(\sum_{i=0}^8{ }_8 C_i(-1)^{8-i} f(x+(i-4) y)=0\)
which is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation, the quintic functional equation, and the sextic functional equation. The equation is analysed from the perspective of Hyers-Ulam-Rassias stability.
Keywords: Stability of a functional equation, general septic functional equation, general septic mapping