Summary.
For a group \( (G, \cdot) \) and a real or complex inner product space \( (E, \langle\cdot, \cdot\rangle) \) with norm \( \def\lr{[\!]} \lr.\lr \) we consider the functional inequality
and describe situations in which (I) implies the Jordan-von Neumann parallelogram equation
.
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Manuscript received: January 18, 2002 and, in final form, August 20, 2002
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Rätz, J. On inequalities associated with the Jordan-von Neumann functional equation . Aequat. Math. 66, 191–200 (2003). https://doi.org/10.1007/s00010-003-2684-8
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DOI: https://doi.org/10.1007/s00010-003-2684-8