General Solution and Generalized Ulam-Hyers Stability of a Generalized 3-Dimensional AQCQ Functional Equation
Authors :
John M. Rassias a, M. Arunkumar, b,∗ and N. Mahesh Kumar c
Author Address :
a Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, Athens 15342, Greece.
b Department of Mathematics, Government Arts College, Tiruvannamalai, TamilNadu, India - 606 603.
c Department of Mathematics, Arunai Engineering College, Tiruvannamalai, TamilNadu, India - 606 603.
*Corresponding author
Abstract :
In this paper, we achieve the general solution and generalized Ulam-Hyers stability of a generalized 3-dimensional AQCQ functional equation
$$\begin{array}{l}
{f\left(x+r(y+z)\right)+f\left(x-r(y+z)\right)}
%\\ {\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \,
=r^{2} \left[f\left(x+y+z\right)+f\left(x-y-z\right)\right]
+2\left(1-r^{2} \right)f\left(x\right) \\
{\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, +\frac{\left(r^{4} -r^{2} \right)}{12} \left[f\left(2(y+z)\right)+f\left(-2(y+z)\right)-4f\left(y+z\right)-4f\left(-(y+z)\right)\right]} \end{array}$$
for all positive integers $r$ with $r\ge 2$ in Banach Space using two different methods.
Keywords :
Additive functional equations, quadratic functional equations, cubic functional equations, Quartic functional equations, mixed type functional equations, generalized Ulam - Hyers stability, fixed p
DOI :
Article Info :
Received : August 10, 2016; Accepted : December 12, 2016.
