On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces

Abstract

In this paper, we establish the general solution of the functional equationfor fixed integers n with n = 0, ±1 and investigate the generalized Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.

A fixed point approach to the stability of an AQCQ-functional equation in RN-spaces

“…It was shown in Lemma 2.1 of [15] that g(x) := f (2x) − 4f (x) and h(x) := f (2x) − 16f (x) are quartic and quadratic, respectively, and that…”

Approximate Euler-Lagrange quadratic mappings

“…Thus, we consider general solutions of Equation (4) for any fixed integer k with |k| > 1 in the following theorem. The following lemma can be found in [25][26][27].…”

“…Suppose on the contrary that there exist a quadratic function Q : R R and a constant b > 0 satisfying (26). Since f is bounded and continuous for all x R, Q is bounded on any open interval containing the origin and continuous at the origin.…”

Stability of the general form of quadratic-quartic functional equations in non-Archimedean $\mathcal{L}$-fuzzy normed spaces

“…In [16], Gordj et al obtained the general solution and investigated the Ulam stability problem for the following mixed quadratic and quartic functional equation…”