SOME STUDIES ON EULER-LAGRANGE QUARTIC FUNCTIONAL EQUATIONS IN β-NORMED SPACES

In this paper, we study two types of Euler-Lagrange functional equations that map $ \jmath $ from normed spaces to $ \beta $-normed spaces using quartic functional equations. We will investigate the inequality under various transformations and perturbations using both fixed point and direct methods, to establish the Hyers-Ulam stability of quartic Euler-Lagrange functional equations.