On some alternative quadratic equations
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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 Classification39B52 39B22
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- Dhombres J., Sme aspects of functional equations, Chulalongkorn Univ. Bangkok, 1979.Google Scholar