Solution and stability of Euler-Lagrange-Rassias quartic functional equations in various quasinormed spaces (Q2319246)

Summary: We obtain the general solution of Euler-Lagrange-Rassias quartic functional equation of the following \(f \left(a x + b y\right) + f \left(b x + a y\right) +(1 / 2) a b(a - b)^2 f(x - y) = (a^2 - b^2)^2 \left[f \left(x\right) + f \left(y\right)\right] +(1 / 2) a b(a + b)^2 f(x + y)\). We also prove the Hyers-Ulam-Rassias stability in various quasinormed spaces when \(b = 1\).