Geodesic
Minimum of a functional in a metric space and fixed points
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1167-1174 
A. V. Arutyunov; B. D. Gel'man. Minimum of a functional in a metric space and fixed points. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1167-1174. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a3/
@article{ZVMMF_2009_49_7_a3,
     author = {A. V. Arutyunov and B. D. Gel'man},
     title = {Minimum of a~functional in a~metric space and fixed points},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1167--1174},
     year = {2009},
     volume = {49},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a3/}
}
TY  - JOUR
AU  - A. V. Arutyunov
AU  - B. D. Gel'man
TI  - Minimum of a functional in a metric space and fixed points
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 1167
EP  - 1174
VL  - 49
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a3/
LA  - ru
ID  - ZVMMF_2009_49_7_a3
ER  - 
%0 Journal Article
%A A. V. Arutyunov
%A B. D. Gel'man
%T Minimum of a functional in a metric space and fixed points
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 1167-1174
%V 49
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a3/
%G ru
%F ZVMMF_2009_49_7_a3

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

The existence of minimizers is examined for a function defined on a metric space. Theorems are proved that assert the existence of minimizers, and examples of the functions for which these theorems are valid are given. Then, these theorems are applied to proving theorems on fixed points of univalent and multivalued mappings of metric spaces. Finally, coincident points of two mappings are examined.

[1] Arutyunov A. B., “Nakryvayuschie otobrazheniya metricheskikh prostranstv i nepodvizhnye tochki”, Dokl. RAN, 416:2 (2007), 151–155 | MR | Zbl

[2] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | MR | Zbl

[3] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988 | MR | Zbl

[4] Fomenko T. N., “O priblizhenii k tochkam sovpadeniya i obschim nepodvizhnym tochkam nabora otobrazhenii metricheskikh prostranstv”, Matem. zametki, 86:1 (2009), 110–125 | MR | Zbl

[5] Nadler S. B., “Multi-valued contraction mappings”, Pasif. J. Math., 30:2 (1969), 475–488 | MR | Zbl