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
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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.
@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},
publisher = {mathdoc},
volume = {49},
number = {7},
year = {2009},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a3/ %G ru %F ZVMMF_2009_49_7_a3
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/