Generalized Ulam - Hyers Stability of on (AQQ): Additive - Quadratic - Quartic  Functional Equation

John M. Rassias a , M. Arunkumar b , E.Sathya c , N. Mahesh Kumar d ∗

Generalized Ulam - Hyers Stability of on (AQQ): Additive - Quadratic - Quartic Functional Equation

Authors :

John M. Rassias ^a , M. Arunkumar^b , E.Sathya^c , N. Mahesh Kumar ^{d ∗}

Author Address :

^a Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, Athens 15342, Greece.
^b,cDepartment of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.
^dDepartment of Mathematics, Arunai Engineering College, Tiruvannamalai - 606 603, TamilNadu, India.

*Corresponding author

Abstract :

In this paper, the authors obtain the general solution and generalized Ulam - Hyers stability of an (AQQ): additive - quadratic - quartic functional equation of the form
\begin{align*}
f(x+y+z)&+f(x+y-z)+f(x-y+z)+f(x-y-z)\notag\\
& = 2\left[f(x+y)+f(x-y)+f(y+z)+f(y-z)+f(x+z)+f(x-z)\right]\notag\\
&\qquad \qquad \qquad -4f(x)-4f(y)-2\left[f(z)+f(-z)\right]
\end{align*}
by using the classical Hyers’ direct method. Counter examples for non stability are discussed also.

Keywords :

Additive functional equations, Quadratic functional equations, Quartic functional equations, Mixed type functional equations, Ulam - Hyers stability, Ulam - Hyers - Rassias stability, Ulam - Gavru

DOI :

Article Info :

Received : September 17, 2016; Accepted : December 10, 2016.