Geodesic
Second-Order Gâteaux Differentiable Bump Functions and Approximations in Banach Spaces
Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 612-625

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we study approximations of convex functions by twice Gâteaux differentiate convex functions. We prove that convex functions (respectively norms) can be approximated by twice Gâteaux differentiate convex functions (respectively norms) in separable Banach spaces which have the Radon-Nikody m property and admit twice Gâteaux differentiable bump functions. New characterizations of spaces isomorphic to Hilbert spaces are shown. Locally uniformly rotund norms that are limits of Ck -smooth norms are constructed in separable spaces which admit Ck -smooth norms.
DOI : 10.4153/CJM-1993-032-9
Mots-clés : 46B20, 46B22, 46C05 
McLaughlin, D.; Poliquin, R.; Vanderwerff, J.; Zizler, V. Second-Order Gâteaux Differentiable Bump Functions and Approximations in Banach Spaces. Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 612-625. doi: 10.4153/CJM-1993-032-9
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