ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION

Title & Authors
ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION
Chung, Jukang-K.; Sahoo, Prasanna, K.;

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, $\small{y\;\in\;\mathbb{R}}$ 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;
Language
English
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