## Abstract and Applied Analysis

### Solution and Stability of Euler-Lagrange-Rassias Quartic Functional Equations in Various Quasinormed Spaces

#### Abstract

We obtain the general solution of Euler-Lagrange-Rassias quartic functional equation of the following $f(ax+by)+f(bx+ay)+(\mathrm{1}/\mathrm{2})ab(a-b{)}^{\mathrm{2}}f(x-y)=({a}^{\mathrm{2}}-{b}^{\mathrm{2}}{)}^{\mathrm{2}}[f(x)+f(y)]+(\mathrm{1}/\mathrm{2})ab(a+b{)}^{\mathrm{2}}f(x+y)\mathrm{}$. We also prove the Hyers-Ulam-Rassias stability in various quasinormed spaces when $b=\mathrm{1}\mathrm{}$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 908168, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393448671

Digital Object Identifier
doi:10.1155/2013/908168

Mathematical Reviews number (MathSciNet)
MR3124026

Zentralblatt MATH identifier
07095480

#### Citation

Koh, Heejeong; Kang, Dongseung. Solution and Stability of Euler-Lagrange-Rassias Quartic Functional Equations in Various Quasinormed Spaces. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 908168, 8 pages. doi:10.1155/2013/908168. https://projecteuclid.org/euclid.aaa/1393448671

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