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ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION

  • Chung, Jukang-K. ;
  • Sahoo, Prasanna, K.
  • Published : 2003.11.01

Abstract

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].

Keywords

additive function;difference operator;Frechet functional equation;n-additive function;quartic map;and quartic functional equation

References

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  2. Glasnik Matematicki v.34 no.54;2 Solution of the Ulam stability problem for quartic mappings J.M.Rassias
  3. Convolution type functional equation on topological abelian groups L.Szekelyhidi
  4. Functional equations in several variables J.Aczel;J.Dhombres
  5. Symmetric second differences in product form on groups. Topics in mathematical analysis J.Aczel;J.K.Chung;C.T.Ng
  6. Bul. Isnt. Politech. Iasi v.10 no.1-2 On the Frechet's functional equation M.Hosszu

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