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

Jung Rye Lee, Choonkil Park, Yeol Je Cho, Dong Yun Shin

Research output: Contribution to journalArticle

11 Citations (Scopus)

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 languageEnglish
Pages (from-to)572-583
Number of pages12
JournalJournal of Computational Analysis and Applications
Volume15
Issue number3
StatePublished - 2013 May 3

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Hyers-Ulam Stability
Fixed Point Method
Banach spaces
Quartic
Orthogonality
Functional equation
Banach space

Keywords

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

Cite this

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

In: Journal of Computational Analysis and Applications, Vol. 15, No. 3, 03.05.2013, p. 572-583.

Research output: Contribution to journalArticle

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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.

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