Stability of Two Types of Cubic Functional Equations in Non-Archimedean Spaces
Mohammad Sal Moslehian and Ghadir Sadeghi
Source: Real Anal. Exchange Volume 33, Number 2
(2007), 375-384.
Abstract
We prove the generalized stability of the cubic type functional equation $$f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$$ and another functional equation $$f(ax+y)+f(x+ay)=(a+1)(a-1)^{2}[f(x)+f(y)] +a(a+1)f(x+y),$$ where $a$ is an integer with $a \neq 0, \pm 1$ in the framework of non-Archimedean normed spaces.
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Keywords: generalized Hyers-Ulam stability; cubic functional equation; non-Archimedean space; $p$-adic field
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rae/1229619415
Mathematical Reviews number (MathSciNet): MR2458254
Zentralblatt MATH identifier: 05499476
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