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http://dx.doi.org/10.14317/jami.2012.30.5_6.829

ON SOLUTIONS AND STABILITY OF A GENERALIZED QUADRATIC EQUATION ON NON-ARCHIMEDEAN NORMED SPACES  

Janfada, Mohammad (Department of Pure Mathematics, Ferdowsi University of Mashhad)
Shourvarzi, Rahele (Department of Mathematics, Sabzevar Tarbiat Moallem University)
Publication Information
Journal of applied mathematics & informatics / v.30, no.5_6, 2012 , pp. 829-845 More about this Journal
Abstract
In this paper we study general solutions and generalized Hyers-Ulam-Rassias stability of the following function equation $$f(x-\sum^{k}_{i=1}x_i)+(k-1)f(x)+(k-1)\sum^{k}_{i=1}(x_i)=f(x-x_1)+\sum^{k}_{i=2}f(x_i-x)+\sum^{k}_{i=1}\sum^{k}_{j=1,j > i}f(x_i+x_j)$$. 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 norm;
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