Eine Parallelogrammungleichung zum Exponenten \(\gamma\) \(\in [1,2]\) für Normen. (A parallelogramm inequality to the exponent \(\gamma\) \(\in [1,2]\) for norms) (Q1076283)

Summary: For a Hilbert space X the generalized parallelogramm inequality to the exponent \(\gamma\) \[ \lambda \| x_ 1\|^{\gamma}+(1- \lambda)\| x_ 2\|^{\gamma}\leq \| \lambda x_ 1+(1- \lambda)x_ 2\|^{\gamma}+mi\quad n\{\lambda,1-\lambda \}C(\gamma)\| x_ 1-x_ 2\|^{\gamma} \] for every \(x_ 1,x_ 2\in X\), \(\lambda\in [0,1]\), \(\gamma\in [1,2]\) is proved and the constant C(\(\gamma)\) is determined. The extension of this inequality to certain normed spaces is possible with restrictions of the parameter \(\gamma\).