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Zeitschrift für Analysis und ihre Anwendungen


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Volume 5, Issue 1, 1986, pp. 71–83
DOI: 10.4171/ZAA/181

Published online: 1986-02-28

Eine Parallelogrammungleichung zum Exponenten $\gamma \in [1, 2]$ für Normen

Armin Hoffmann[1]

(1) TU Ilmenau, Germany

For a Hilbert space $X$ the generalized parallelogramm inequality to the exponent $\gamma$ $$\lambda \| x_1 \|^\gamma + (1-\lambda) \|x_2\| \leq \|\lambda x_1 + (1-\lambda) x_2\|^\gamma + \mathrm {min} \{ \lambda, 1-\lambda\} C (\gamma) \|x_1 - x_2\|^\gamma$$ 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 $\gamma$.

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Hoffmann Armin: Eine Parallelogrammungleichung zum Exponenten $\gamma \in [1, 2]$ für Normen. Z. Anal. Anwend. 5 (1986), 71-83. doi: 10.4171/ZAA/181