IJPAM: Volume 106, No. 5 (2016)

GENERALIZED HYERS-ULAM STABILITY FOR
A MIXED ADDITIVE-QUADRATIC-CUBIC-QUARTIC
(AQCQ) FUNCTIONAL EQUATION IN
QUASI-BANACH SPACES

K. Balamurugan$^1$, M. Arunkumar$^2$, P. Ravindiran$^3$
$^{1,2}$Department of Mathematics
Govt. Arts College
Tiruvannamalai, 606 603, TamilNadu, INDIA
$^3$Department of Mathematics
A.A. Govt. Arts College
Villupuram, 605 602, Tamilnadu, INDIA


Abstract. In this paper we establish the general solution and investigate the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation
\begin{align}
&f(3x+2y+z) + f(3x+2y-z) + f(3x-2y+z) + f(3x-2y-z) \notag\\ &=48[f...
...otag \\ &\quad-80f(-x)+ 2\tilde{f}(2y)-80\tilde{f}(y)-24\tilde{f}(z)
\end{align}
in quasi-Banach spaces where $\tilde{f}(x)=f(x)+f(-x)$.

Received: January 23, 2016

AMS Subject Classification: 39B52, 39B72, 39B82

Key Words and Phrases: Hyers-Ulam stability, additive-quadratic-cubic-quartic mapping, mixed type functional equation, quasi - Banach space, p - Banach space

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DOI: 10.12732/ijpam.v106i5.10 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 5
Pages: 99 - 121


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