We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x - my) = 2(7m - 9)(m - 1)f(x) + 2m²(m² - 1)f(y)-(m - 1)² f(2x) + m²{f(x + y) + f(x - y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stab...

In this paper, we define the multicubic-quartic and multimixed cubic-quartic mappings characterize them. other words, unify system of functional equations defining a (resp., multicubic-quartic) mapping to single equation, namely, equation. We also show that under what conditions can be multicubic, multiquartic multicubic-quartic. Moreover, by using fixed point theorem, study generalized Hyers-U...