Geodesic
A criterion of smooth generating sets
Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 343-368 
G. E. Ivanov. A criterion of smooth generating sets. Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 343-368. http://geodesic.mathdoc.fr/item/SM_2007_198_3_a1/
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For a smooth strictly convex set in a reflexive Banach space a criterion is given for this set to be generating. This criterion enabled us to discover new classes of generating sets. Bibliography: 6 titles.

[1] E. S. Polovinkin, “O novykh klassakh porozhdayuschikh mnozhestv”, Nekotorye problemy fundamentalnoi i prikladnoi matematiki, Mezhduved. sb., MFTI, M., 1998, 81–93

[2] E. S. Polovinkin, M. V. Balashov, Elementy vypuklogo i silno vypuklogo analiza, Fizmatlit, M., 2004

[3] M. V. Balashov, E. S. Polovinkin, “$M$-silno vypuklye mnozhestva i ikh porozhdayuschie podmnozhestva”, Matem. sb., 191:1 (2000), 27–64 ; M. V. Balashov, E. S. Polovinkin, “$M$-strongly convex subsets and their generating sets”, Sb. Math., 191:1 (2000), 25–60 ; 81–93 | MR | Zbl | DOI

[4] R. N. Karasev, “O kharakterizatsii porozhdayuschikh mnozhestv”, Modelirovanie i analiz informatsionnykh sistem, 8:2 (2001), 3–9 | MR

[5] B. M. Makarov, M. G. Goluzina, A. A. Lodkin, A. N. Podkorytov, Izbrannye zadachi po veschestvennomu analizu, BKhV, SPb., 2004 ; B. M. Makarov, M. G. Goluzina, A. A. Lodkin, A. N. Podkorytov, Selected problems in real analysis, Transl. Math. Monogr., 107, Amer. Math. Soc., Providence, RI, 1992 | MR | Zbl | MR | Zbl

[6] U. Rudin, Funktsionalnyi analiz, Mip, M., 1975 ; W. Rudin, Functional analysis, McGraw-Hill, New York, 1973 | MR | MR | Zbl