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On the differentiability of norms in Banach spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 161، دوره 13، شماره 2، مهر 2022، صفحه 2015-2023 اصل مقاله (370.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.22114.2329 | ||
| نویسنده | ||
| Andres Felipe Munoz-Tello* | ||
| Faculty of Basic Sciences, Santiago de Cali University, Valle del Cauca, Cali, Colombia | ||
| تاریخ دریافت: 23 مهر 1399، تاریخ بازنگری: 26 آذر 1399، تاریخ پذیرش: 06 دی 1399 | ||
| چکیده | ||
| The purpose of this paper is to show some particularities that the differentiability sets generated from the norms have in the Banach spaces. In this sense, it will be shown that the Gaussian measure of the Fr'echet differentiability set of the norm of the space $\ell^{\infty}(\mathbb{R})$ of real bounded sequences is zero and that in the case of the space $BV[a,b]$ of bounded variation functions its norm is not Fr'echet derivable in any element of this space. | ||
| کلیدواژهها | ||
| Gâteaux differentiable؛ Fréchet differentiable؛ locally Lipschitz function؛ Gauss null set | ||
| مراجع | ||
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