• Title, Summary, Keyword: Frechet functional equation

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ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION

  • Chung, Jukang-K.;Sahoo, Prasanna, K.
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.4
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    • pp.565-576
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    • 2003
  • In this paper, we determine the general solution of the quartic equation f(x+2y)+f(x-2y)+6f(x) = 4[f(x+y)+f(x-y)+6f(y)] for all x, $y\;\in\;\mathbb{R}$ without assuming any regularity conditions on the unknown function f. The method used for solving this quartic functional equation is elementary but exploits an important result due to M. Hosszu [3]. The solution of this functional equation is also determined in certain commutative groups using two important results due to L. Szekelyhidi [5].