The functional equation /(y -x) -g{xy) = h (l/i -1/y) is solved for general solution. The result is then applied to show that the three functional equations f{xy) = f(x) + f{y), f{y-x)-f{xy) = /(1/x-l/y) and f{y-x)-f{x) -f(y) = f{l/x -l/y) are equivalent. Finally, twice differentiable solution functions of the functional equation f{y -i) -gi{x) -g2(y) = h {l/x -\/y) are determined. 2010 Mathematics Subject Classification: primary 39B20.
Abstract. We determine the general solution of the generalized additivequartic 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 : R → R and its stability is investigated.
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