Preprint Article Version 1 This version is not peer-reviewed

# A General Theorem on the Stability of a Class of Functional Equations including Quartic-Cubic-Quadratic-Additive Equations

Version 1 : Received: 21 October 2018 / Approved: 22 October 2018 / Online: 22 October 2018 (14:29:00 CEST)

A peer-reviewed article of this Preprint also exists.

Lee, Y.-H.; Jung, S.-M. A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations. Mathematics 2018, 6, 282. Lee, Y.-H.; Jung, S.-M. A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations. Mathematics 2018, 6, 282.

Journal reference: Mathematics 2018, 6, 282
DOI: 10.3390/math6120282

## Abstract

We prove general stability theorems for $n$-dimensional quartic-cubic-quadratic-additive type functional equations of the form \begin{eqnarray*} \sum_{i=1}^\ell c_i f \big( a_{i1}x_1 + a_{i2}x_2 + \cdots + a_{in}x_n \big) = 0 \end{eqnarray*} by applying the direct method. These stability theorems can save us much trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

## Subject Areas

generalized Hyers-Ulam stability; functional equation; $n$-dimensional quartic-cubic-quadratic-additive type functional equation; direct method