Preprint Article Version 1 This version is not peer-reviewed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

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