# STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN QUASI-BANACH SPACES

• Najati, Abbas (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCES UNIVERSITY OF MOHAGHEGH ARDABILI) ;
• Moradlou, Fridoun (FACULTY OF MATHEMATICAL SCIENCES UNIVERSITY OF TABRIZ)
• Published : 2008.08.31

#### Abstract

In this paper we establish the general solution and investigate the Hyers-Ulam-Rassias stability of the following functional equation in quasi-Banach spaces. $${\sum\limits_{{{1{\leq}i<j{\leq}4}\limits_{1{\leq}k<l{\leq}4}}\limits_{k,l{\in}I_{ij}}}\;f(x_i+x_j-x_k-x_l)=2\;\sum\limits_{1{\leq}i<j{\leq}4}}\;f(x_i-x_j)$$ where $I_{ij}$={1, 2, 3, 4}\backslash${i, j} for all$1{\leq}i<j{\leq}4\$. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.

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