A generalized additive-quartic functional equation and its stability
Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 1759-1776
https://doi.org/10.4134/BKMS.2015.52.6.1759
Published online November 30, 2015
Charinthip Hengkrawit and Anurak Thanyacharoen
Thammasat University, Muban Chombueng Rajabhat University
Abstract : We determine the general solution of the generalized additive-quartic functional equation $f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)-13\left[f(x+y)+f(x-y)\right]+24f(y)-12f(2y) = 0$ without assuming any regularity conditions on the unknown function $f : \R \to \R$ and its stability is investigated.
Keywords : functional equation, Fr\'{e}chet functional equation, additive function, quartic function, difference operator, stability
MSC numbers : 39B22, 39B82
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