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A GENERALIZED ADDITIVE-QUARTIC FUNCTIONAL EQUATION AND ITS STABILITY

  • HENGKRAWIT, CHARINTHIP (Department of Mathematics and Statistics Faculty of Science and Technology Thammasat University) ;
  • THANYACHAROEN, ANURK (Department of Mathematics Faculty of Science and Technology Muban Chombueng Rajabhat University)
  • Received : 2013.01.29
  • Published : 2015.11.30

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 [f(x + y) + f(x - y)] + 24f(y) - 12f(2y) = 0 without assuming any regularity conditions on the unknown function f : ${\mathbb{R}}{\rightarrow}{\mathbb{R}}$ and its stability is investigated.

Keywords

functional equation;$Fr{\acute{e}}chet$ functional equation;additive function;quartic function;difference operator;stability

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