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Results in Mathematics

, Volume 27, Issue 3–4, pp 402–411 | Cite as

On some alternative quadratic equations

  • Fulvia Skof
Article
  • 7 Downloads

Abstract

From the quadratic functional equation ƒ(x + y) + ƒ(x − y) 2ƒ(x) 2f(y) = 0 various alternative equations are derived here by grouping in different ways its terms and then equating norms. Some equivalence results are proved in the class of functionals ƒ: X → (ℝ, ¦· ¦). Suitable examples concerning operators ƒ: X → (E,∥· ∥) with values in normed spaces show that in this more general setting such an equivalence can fail to be true.

AMS 1991 Math. Subject Classification

39B52 39B22 

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References

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    Aczél J., Dhombres J., Functional equations in several variables, Cambridge University Press, Cambridge, 1989.MATHCrossRefGoogle Scholar
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    Dhombres J., Sme aspects of functional equations, Chulalongkorn Univ. Bangkok, 1979.Google Scholar
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    Ger R., On a characterization of strictly convex spaces, Atti Accad. Sc. Torino, 127 (1993), 131–138.MathSciNetMATHGoogle Scholar
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    Skof F., On the functional equation ∥ƒ(x + y) − ƒ(x) = ∥ƒ(y)∥, Atti Accad. Sc. Torino, 127 (1993), 229–237.MathSciNetMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1995

Authors and Affiliations

  • Fulvia Skof
    • 1
  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItalia

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