Jensen type quadratic-quadratic mapping in Banach spaces

Choonkil Park, Seong Ki Hong, Myoung Jung Kim

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Let X, Y be vector spaces. It is shown that if an even mapping f : X → Y satisfies f(0) = 0 and f(x + y/2 + z) + f(x + y/2 - z) + f(x - y/2 + z) (0.1) + f(x - y/2 - z) = f(x) + f(y) + 4f(z) for all x, y, z ∈ X, then the mapping f : X → Y is quadratic. Furthermore, we prove the Cauchy-Rassias stability of the functional equation (0.1) in Banach spaces.

Original languageEnglish
Pages (from-to)703-709
Number of pages7
JournalBulletin of the Korean Mathematical Society
Volume43
Issue number4
DOIs
StatePublished - 2006 Nov

Keywords

  • Cauchy Rassias stability
  • Functional equation
  • Quadratic mapping

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