STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN QUASI-BANACH SPACES

Title & Authors
STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN QUASI-BANACH SPACES

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. $\small{{\sum\limits_{{{1{\leq}i}$<$\small{j{\leq}4}\limits_{1{\leq}k}$<$\small{l{\leq}4}}\limits_{k,l{\in}I_{ij}}}\;f(x_i+x_j-x_k-x_l)=2\;\sum\limits_{1{\leq}i}$<$\small{j{\leq}4}}\;f(x_i-x_j)}$ where $\small{I_{ij}}$={1, 2, 3, 4}$\small{\backslash}${i, j} for all $\small{1{\leq}i}$<$\small{j{\leq}4}$. 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.
Keywords
Language
English
Cited by
1.
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2.
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3.
Approximate Behavior of Bi-Quadratic Mappings in Quasinormed Spaces, Journal of Inequalities and Applications, 2010, 2010, 1, 472721
4.
Generalized Stability of Euler-Lagrange Quadratic Functional Equation, Abstract and Applied Analysis, 2012, 2012, 1
5.
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