## Abstract and Applied Analysis

### Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces

#### Abstract

We obtain the general solution of the generalized mixed additive and quadratic functional equation $f(x+my)+f(x-my)=2f(x)-2{m}^{2}f(y)+{m}^{2}f(2y)$, $m$ is even; $f(x+y)+f(x-y)-2({m}^{2}-1)f(y)+({m}^{2}-1)f(2y)$, $m$ is odd, for a positive integer $m$. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces when $m$ is an even positive integer or $m=3$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 198018, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393448673

Digital Object Identifier
doi:10.1155/2013/198018

Mathematical Reviews number (MathSciNet)
MR3121484

Zentralblatt MATH identifier
1291.39039

#### Citation

Bodaghi, Abasalt; Kim, Sang Og. Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 198018, 10 pages. doi:10.1155/2013/198018. https://projecteuclid.org/euclid.aaa/1393448673

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