Geodesic
Uniform Convexity in Nonsymmetric Spaces
Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 773-785.

Voir la notice de l'article provenant de la source Math-Net.Ru

Uniformly convex asymmetric spaces are defined. It is proved that every nonempty closed convex set in a uniformly convex complete asymmetric space is a set of approximative uniqueness (and, in particular, a Chebyshev set).
Keywords: asymmetric spaces, approximative uniqueness, uniform convexity. 
@article{MZM_2021_110_5_a11,
     author = {I. G. Tsar'kov},
     title = {Uniform {Convexity} in {Nonsymmetric} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {773--785},
     publisher = {mathdoc},
     volume = {110},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a11/}
}
TY  - JOUR
AU  - I. G. Tsar'kov
TI  - Uniform Convexity in Nonsymmetric Spaces
JO  - Matematičeskie zametki
PY  - 2021
SP  - 773
EP  - 785
VL  - 110
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a11/
LA  - ru
ID  - MZM_2021_110_5_a11
ER  - 
%0 Journal Article
%A I. G. Tsar'kov
%T Uniform Convexity in Nonsymmetric Spaces
%J Matematičeskie zametki
%D 2021
%P 773-785
%V 110
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a11/
%G ru
%F MZM_2021_110_5_a11
I. G. Tsar'kov. Uniform Convexity in Nonsymmetric Spaces. Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 773-785. http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a11/

[1] Ş. Cobzaş, Functional Analysis in Asymmetric Normed Spaces, Front. Math., Birkhäuser/Springer Basel AG, Basel, 2013 | DOI | MR | Zbl

[2] S. Cobzaş, “Separation of convex sets and best approximation in spaces with asymmetric norm”, Quaest. Math., 27:3 (2004), 275–296 | MR | Zbl

[3] A. R. Alimov, “Teorema Banakha–Mazura dlya prostranstv s nesimmetrichnym rasstoyaniem”, UMN, 58:2 (350) (2003), 159–160 | DOI | MR | Zbl

[4] A. R. Alimov, “O strukture dopolneniya k chebyshevskim mnozhestvam”, Funkts. analiz i ego pril., 35:3 (2001), 19–27 | DOI | MR | Zbl

[5] A. R. Alimov, “Vypuklost ogranichennykh chebyshevskikh mnozhestv v konechnomernykh prostranstvakh s nesimmetrichnoi normoi”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4 (2) (2014), 489–497 | DOI | Zbl

[6] I. G. Tsarkov, “Approksimativnye svoistva mnozhestv i nepreryvnye vyborki”, Matem. sb., 211:8 (2020), 132–157 | DOI | Zbl

[7] I. G. Tsarkov, “Slabo monotonnye mnozhestva i nepreryvnaya vyborka v nesimmetrichnykh prostranstvakh”, Matem. sb., 210:9 (2019), 129–152 | DOI | MR | Zbl

[8] I. G. Tsarkov, “Nepreryvnye vyborki iz operatorov metricheskoi proektsii i ikh obobschenii”, Izv. RAN. Ser. matem., 82:4 (2018), 199–224 | DOI | MR | Zbl

[9] I. G. Tsarkov, “Nepreryvnye vyborki v nesimmetrichnykh prostranstvakh”, Matem. sb., 209:4 (2018), 95–116 | DOI | MR | Zbl