Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type $f(x+y)+g(x-y)=h(x)+k(y)$, where $f, g, h, k$ are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on $f$.

A Fixed Point Approach to Stability of a Quadratic Equation

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation: in fuzzy Banach spaces.

/pdf/random-stability-of-an-additive-quadratic-quartic-functional-3hi0ry3kpy.pdf

Random Stability of an Additive-Quadratic-Quartic Functional Equation

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation $$f(2x+y)+f(2x-y)=4(f(x+y)+f(x-y))-{3/7}(f(2y)-2f(y))+2f(2x)-8f(x).$$

Stability of a functional equation deriving from quartic and additive functions

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation f(2x + y) + f(2x - y) = 4(f(x + y) + f(x - y)) - (f(2y) - 2f(y)) + 2f(2x) - 8f(x).

/pdf/stability-of-a-functional-equation-deriving-from-quartic-and-25bpnqlp6b.pdf

We prove the generalized Hyers-Ulam stability of the following additive-cubic-quartic functional equation: in complete latticetic random normed spaces.

/pdf/nonlinear-random-stability-of-an-acq-functional-equation-3rvkwxqr1y.pdf

Nonlinear -Random Stability of an ACQ Functional Equation

In this paper, we consider the additive-cubic-quartic functional equation and prove the generalized Hyers-Ulam stability of the additive-cubic-quartic functional equation in Banach spaces.

https://link.springer.com/content/pdf/10.1155%2F2009%2F395693.pdf

Stability of an Additive-Cubic-Quartic Functional Equation

We find the general solution of the functional equation 

$$\begin{array}{l} D_f {\rm{(}}x,y{\rm{)}}\,\,{\rm{: = }}f{\rm{(}}x + {\rm{2}}y{\rm{)}} + f{\rm{(}}x - {\rm{2}}y{\rm{)}} - {\rm{4[}}f{\rm{(}}x + y{\rm{)}} - f{\rm{(}}x - y{\rm{)]}} - f{\rm{(4}}y{\rm{)}} + {\rm{4}}f{\rm{(3}}y{\rm{)}} \\ - {\rm{6}}f{\rm{(2}}y{\rm{)}} + {\rm{4}}f{\rm{(}}y{\rm{)}} + {\rm{6}}f{\rm{(}}x{\rm{) }} = {\rm{ 0}}{\rm{.}} \\ \end{array}$$

in the context of linear spaces. We prove that if a mapping f from a linear space X into a Banach space Y satisfies f(0)=0 and 

$$\|D_f(x,y)\|\leq\epsilon \quad (x,y\in X),$$

where e > 0, then there exist a unique additive mapping $A:X\to Y,$ a unique quadratic mapping $Q_1:X\to Y,$ a unique cubic mapping $C:X\to Y$ and a unique quartic mapping $Q_2:X\to Y$ such that 

$$\|f(x)-A(x)-Q_1(x)-C(x)-Q_2(x)\|\leq\frac{1087 \epsilon}{140}\quad \forall x\in X.$$

M. Eshaghi-Gordji

Papers

Stability of an Additive-Cubic-Quartic Functional Equation

Stability of a Mixed Type Additive, Quadratic, Cubic and Quartic Functional Equation