대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제34권4호
  • /
  • Pages.561-571
  • /
  • 1997
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

On solution and stability of functional equation $f(x+y)^2=af(x)f(y)+bf(x)^2+cf(y)^2$

  • Jung, Soon-Mo (Mathematics Section, College of Science & Technology, Hong-Ik University, Chochiwon 339-800)
  • 발행 : 1997.11.01
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초록

The general (continuous) solution and the asymptotic behaviors of the unbounded solution of the functional equation $f(x + y)^2 = af(x)f(y) + bf(x)^2 + cf(y)^2$ and the Hyers-Ulam stability of that functional equation for the case when a = 2 and b = c = 1 shall be investigated.

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참고문헌

  1. Aeq. Math. v.35 Relations de dependence entre les equations fonctionnelles de Cauchy J. Dhombres
  2. Proc. Nat. Acad. Sci. U.S.A. v.27 On the stability of the linear functional equation D.H. Hyers
  3. Proc. Amer. Math. Soc. v.19 The functional equation f(xy)+$f(xy^{-1})$=2f(x)f(y) for groups Pl. Kannappan
  4. Warszawa-Krakow:Panstwo-we Wydawnictwo Naukowe An introduction to the theory of functional equations and inequalities M. Kuczma
  5. Proc. Amer. Math. Soc. v.72 On the stability of the linear mapping in Banach spaces Th. M. Rassias
  6. Aeq. Math. v.45 On two conditional forms of the equation ∥f(x+y)∥=∥f(x)+f(y)∥ F. Skof