### Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of the orthogonally cubic-quartic functional equation f(2x + y) + f(2x - y) = 3f(x + y) + f(-x - y) + 3f(x - y) + f(y - x) +18f(x) + 6f(-x) - 3f(y) - 3f(-y) for all x; y with x ⊥ y in non-Archimedean Banach spaces, where ⊥ is the orthogonality in the sense of Rätz.

Original language | English |
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Pages (from-to) | 572-583 |

Number of pages | 12 |

Journal | Journal of Computational Analysis and Applications |

Volume | 15 |

Issue number | 3 |

State | Published - 2013 May 3 |

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### Keywords

- Fixed point
- Hyers-Ulam stability
- Non-Archimedean normed space
- Orthogonality space
- Orthogonally cubic-quartic functional equation

### Cite this

*Journal of Computational Analysis and Applications*,

*15*(3), 572-583.

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*Journal of Computational Analysis and Applications*, vol. 15, no. 3, pp. 572-583.

**Orthogonal stability of a cubic-quartic functional equation in non-Archimedean spaces.** / Lee, Jung Rye; Park, Choonkil; Cho, Yeol Je; Shin, Dong Yun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Orthogonal stability of a cubic-quartic functional equation in non-Archimedean spaces

AU - Lee, Jung Rye

AU - Park, Choonkil

AU - Cho, Yeol Je

AU - Shin, Dong Yun

PY - 2013/5/3

Y1 - 2013/5/3

N2 - Using the fixed point method, we prove the Hyers-Ulam stability of the orthogonally cubic-quartic functional equation f(2x + y) + f(2x - y) = 3f(x + y) + f(-x - y) + 3f(x - y) + f(y - x) +18f(x) + 6f(-x) - 3f(y) - 3f(-y) for all x; y with x ⊥ y in non-Archimedean Banach spaces, where ⊥ is the orthogonality in the sense of Rätz.

AB - Using the fixed point method, we prove the Hyers-Ulam stability of the orthogonally cubic-quartic functional equation f(2x + y) + f(2x - y) = 3f(x + y) + f(-x - y) + 3f(x - y) + f(y - x) +18f(x) + 6f(-x) - 3f(y) - 3f(-y) for all x; y with x ⊥ y in non-Archimedean Banach spaces, where ⊥ is the orthogonality in the sense of Rätz.

KW - Fixed point

KW - Hyers-Ulam stability

KW - Non-Archimedean normed space

KW - Orthogonality space

KW - Orthogonally cubic-quartic functional equation

UR - http://www.scopus.com/inward/record.url?scp=84876886954&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84876886954

VL - 15

SP - 572

EP - 583

JO - Journal of Computational Analysis and Applications

JF - Journal of Computational Analysis and Applications

SN - 1521-1398

IS - 3

ER -