Solution and Stability of Euler-Lagrange-Rassias Quartic Functional Equations in Various Quasinormed Spaces

Abstract

We obtain the general solution of Euler-Lagrange-Rassias quartic functional equation of the following ( + ) + (We also prove the Hyers-Ulam-Rassias stability in various quasinormed spaces when = 1.

Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN Spaces

“…We were able to refer to some needed preliminaries in the Refs. [28,[30][31][32], and utilized the alternative fixed-point theorem which gave some important results in the fixed-point theory.…”

Ulam Stability of a Mixed Type Additive-Quartic Functional Equation

“…Since then several stability problems for various functional equations have been investigated in (see [1], [3], [4], [9], [11], [12], [13], [15], [19], [20], [21]). Recently, the Ulam stability problem for mixed type additive-quadratic, additivecubic, additive-quartic, quadratic-cubic, quadratic-quartic, cubic-quartic, additive-quadratic-cubic, additive-cubic-quartic, quadratic-cubic-quartic and additive-quadratic-cubic-quartic functional equations have been considered in (see [6], [7], [8], [14], [16], [17], [18]).…”