Journal of Applied Mathematics and Informatics, Volume (30), No (5), Year (2012-6) , Pages (829-845)

#### Title : ( On solutions and stability of a generalized quadratic equation on non-Archimedean normed spaces )

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In this paper we study general solutions and generalized Hyers-Ulam-Rassias stability of the following function equation $$f(x-\\sum_{i=1}^{k}x_{i})+(k-1)f(x)+(k-1)\\sum_{i=1}^{k}f(x_{i}) =f(x-x_{1})+\\sum_{i=2}^{k}f(x_{i}-x)+\\sum_{i=1}^{k}\\sum_{j=1,~j>i}^{k}f(x_{i}+x_{j}),$$ for $k\\geq 2$, on non-Archimedean Banach spaces. It will be proved that this equation is equivalent to the so-called quadratic functional equation.

#### Keywords

, Hyers, , Ulam, , Rassias stability; Quadratic equation; Non, Archimedean
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@article{paperid:1033753,
title = {On solutions and stability of a generalized quadratic equation on non-Archimedean normed spaces},
journal = {Journal of Applied Mathematics and Informatics},
year = {2012},
volume = {30},
number = {5},
month = {June},
issn = {1598-5857},
pages = {829--845},
numpages = {16},
keywords = {Hyers--Ulam--Rassias stability; Quadratic equation; Non-Archimedean norm.},
}