Quadratic functional equation and inner product spaces. (English) Zbl 0836.39006

The aim of the paper is to characterize inner product spaces as those in which the square of the norm satisfies some functional equations. The author considers five such equations. Actually, the equations are solved in general, and in some important cases it is noticed that their only solutions are quadratic functionals (i.e. functionals satisfying the Jordan-von Neumann identity).


39B52 Functional equations for functions with more general domains and/or ranges
39B22 Functional equations for real functions
15A63 Quadratic and bilinear forms, inner products
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