We study various notions of directional moduli of rotundity and when such moduli of rotundity of power type imply the underlying space is superreflexive. Duality with directional moduli of smoothness and some applications are also discussed.
@article{119062, author = {Michael O. Bartlett and John R. Giles and Jon D. Vanderwerff}, title = {Directional moduli of rotundity and smoothness}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {40}, year = {1999}, pages = {39-51}, zbl = {1060.46501}, mrnumber = {1715201}, language = {en}, url = {http://dml.mathdoc.fr/item/119062} }
Bartlett, Michael O.; Giles, John R.; Vanderwerff, Jon D. Directional moduli of rotundity and smoothness. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 39-51. http://gdmltest.u-ga.fr/item/119062/
Second-order differentiability of convex functions in Banach spaces, Trans. Amer. Math. Soc. 342 (1994), 43-81. (1994) | MR 1145959 | Zbl 0802.46027
Partially smooth variational principles and applications, preprint. | MR 1707806 | Zbl 0927.49010
Geometric Aspects of Convex Sets with the Radon-Nikodym Property, Lecture Notes in Mathematics 993, Springer-Verlag, 1983. | MR 0704815 | Zbl 0512.46017
The geometry of Banach spaces. Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284-314. (1964) | MR 0163143 | Zbl 0123.30701
Uniform convexity III, Bull. Amer. Math. Soc. 49 (1943), 745-750. (1943) | MR 0009422 | Zbl 0063.01056
Smoothness and Renormings in Banach Spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics 64, Longman, 1993. | MR 1211634 | Zbl 0782.46019
Smooth bump functions and the geometry of Banach spaces, Mathematika 40 (1993), 305-321. (1993) | MR 1260894
Lipschitz smooth points of convex functions and isomorphic characterizations of Hilbert spaces, Proc. London Math. Soc. 51 (1985), 113-126. (1985) | MR 0788852 | Zbl 0549.46025
On weak Hadamard differentiability of convex functions on Banach spaces, Bull. Austral. Math. Soc. 54 (1996), 155-166. (1996) | MR 1403000 | Zbl 0886.46050
Dual renormings of Banach spaces, Comment. Math. Univ. Carolinae 37 (1996), 241-253. (1996) | MR 1398999
Second-order Gateaux differentiable bump functions and approximations in Banach spaces, Canad. J. Math. 45 (1993), 612-625. (1993) | MR 1222519 | Zbl 0796.46005
Higher-order Gateaux differentiable bump functions on Banach spaces, Bull. Austral. Math. Soc. 51 (1995), 291-300. (1995) | MR 1322795
Generic continuity of minimal set-valued mappings, J. Austral. Math. Soc. 63A (1997), 238-262. (1997) | MR 1475564 | Zbl 0912.46017
Banach spaces that are uniformly rotund in weakly compact sets of directions, Canad. J. Math. 29 (1977), 963-970. (1977) | MR 0450942 | Zbl 0338.46021
A curious generalization of local uniform rotundity, Comment. Math. Univ. Carolinae 25 (1984), 659-665. (1984) | MR 0782015 | Zbl 0578.46017
Normal structure in Banach spaces and its generalisations, Contemporary Mathematics 18 (1983), 201-215. (1983) | MR 0728601 | Zbl 0512.46014
A dual view of a theorem of Ballion, Nonlinear Analysis and Applications, Dekker, New York, 1982, pp.279-286. | MR 0689566
Differentiability of the distance function and points of multivaluedness of the metric projection in Banach spaces, Czech. Math. J. 33 (1983), 292-308. (1983) | MR 0699027