DOI QR코드

DOI QR Code

ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION

  • Chung, Jukang-K. (Department of Applied Mathematics, South China University of Technology) ;
  • Sahoo, Prasanna, K. (Department of Mathematics, University of Louisville)
  • 발행 : 2003.11.01

초록

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].

참고문헌

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

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