Real Analysis Exchange

Stability of Two Types of Cubic Functional Equations in Non-Archimedean Spaces

Mohammad Sal Moslehian and Ghadir Sadeghi

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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.

Article information

Real Anal. Exchange Volume 33, Number 2 (2007), 375-384.

First available: 18 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 39B22: Equations for real functions [See also 26A51, 26B25]
Secondary: 39B82: Stability, separation, extension, and related topics [See also 46A22] 46S10: Functional analysis over fields other than $R$ or $C$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]

generalized Hyers-Ulam stability cubic functional equation non-Archimedean space $p$-adic field


Moslehian, Mohammad Sal; Sadeghi, Ghadir. Stability of Two Types of Cubic Functional Equations in Non-Archimedean Spaces. Real Analysis Exchange 33 (2007), no. 2, 375--384.

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