3 Dimensional Additive Quadratic Functional Equation

M. Arunkumara*, P. Narasimmanb, E.Sathyac, N. Mahesh Kumard

3 Dimensional Additive Quadratic Functional Equation

Authors :

M. Arunkumar^a*, P. Narasimman^b, E.Sathya^c, N. Mahesh Kumar^d

Author Address :

^a,cDepartment of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.
^bDepartment of Mathematics, Thiruvalluvar University College of Arts and Science, Gajalnaickanpatti, Tirupattur-635 901,TamilNadu, India.
^dDepartment of Mathematics, Arunai Engineering College, Tiruvannamalai - 606 603, TamilNadu, India.

*Corresponding author

Abstract :

In this paper, the authors established the general solution and generalized Ulam - Hyers stability of an 3 dimensional additive quadratic functional equation
\begin{align*}
&h(x+2y+3z)+h(x+2y-3z)+h(x-2y+3z)+h(-x+2y+3z)\\
&\qquad\qquad= h(x+y+z)+h(x+y-z)+h(x-y+z)+h(-x+y+z)\\
&\qquad \qquad\qquad\qquad\qquad+ 2h(y)+4h(z)+5[h(y)+h(-y)]+14[h(z)+h(-z)]
\end{align*}
via Banach space and non-Archimedean fuzzy Banach Space using direct and fixed point methods.

Keywords :

Additive functional equation, quadratic functional equation, mixed additive-quadratic functional equations, generalized Ulam - Hyers stability, Banach space, non-Archim

DOI :

Article Info :

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