General solution and generalized Ulam-Hyers stability of a generalized 3-Dimensional AQCQ functional equation

John M. Rassias; M. Arunkumar; N. Mahesh Kumar

doi:10.26637/mjm501/014

Abstract

In this paper, we achieve the general solution and generalized Ulam-Hyers stability of a generalized 3dimensional AQCQ functional equation
$$
\begin{aligned}
&f(x+r(y+z))+f(x- r(y+z))=r^2[f(x+y+z)+f(x-y-z)]\\&+2\left(1-r^2\right) f(x) + \frac{\left(r^4-r^2\right)}{12}[f(2(y+z))+f(-2(y+z))\\&-4 f(y+z)-4 f(-(y+z))]
\end{aligned}
$$
for all positive integers $r$ with $r \geq 2$ 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 point

Mathematics Subject Classification:

39B52, 32B72, 32B82

Authors Imprint References Funding Related Articles Downloads

John M. Rassias Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, Athens 15342, Greece.
M. Arunkumar Department of Mathematics, Government Arts College, Tiruvannamalai, Tamil Nadu, India - 606 603.
N. Mahesh Kumar Department of Mathematics, Arunai Engineering College, Tiruvannamalai, Tamil Nadu, India - 606 603.

Pages: 149-185
Date Published: 01-01-2017
Vol. 5 No. 01 (2017): Malaya Journal of Matematik (MJM)

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