Eurasian mathematical journal, Tome 8 (2017) no. 3, pp. 70-76
Citer cet article
R. Sengupta. On fixed points of contraction maps acting in $(q_1, q_2)$-quasimetric spaces and geometric properties of these spaces. Eurasian mathematical journal, Tome 8 (2017) no. 3, pp. 70-76. http://geodesic.mathdoc.fr/item/EMJ_2017_8_3_a7/
@article{EMJ_2017_8_3_a7,
author = {R. Sengupta},
title = {On fixed points of contraction maps acting in $(q_1, q_2)$-quasimetric spaces and geometric properties of these spaces},
journal = {Eurasian mathematical journal},
pages = {70--76},
year = {2017},
volume = {8},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/EMJ_2017_8_3_a7/}
}
TY - JOUR
AU - R. Sengupta
TI - On fixed points of contraction maps acting in $(q_1, q_2)$-quasimetric spaces and geometric properties of these spaces
JO - Eurasian mathematical journal
PY - 2017
SP - 70
EP - 76
VL - 8
IS - 3
UR - http://geodesic.mathdoc.fr/item/EMJ_2017_8_3_a7/
LA - en
ID - EMJ_2017_8_3_a7
ER -
%0 Journal Article
%A R. Sengupta
%T On fixed points of contraction maps acting in $(q_1, q_2)$-quasimetric spaces and geometric properties of these spaces
%J Eurasian mathematical journal
%D 2017
%P 70-76
%V 8
%N 3
%U http://geodesic.mathdoc.fr/item/EMJ_2017_8_3_a7/
%G en
%F EMJ_2017_8_3_a7
We study geometric properties of $(q_1, q_2)$-quasimetric spaces and fixed point theorems in these spaces. In paper [1], a fixed point theorem was obtained for a contraction map acting in a complete $(q_1, q_2)$-quasimetric space. The graph of the map was assumed to be closed. In this paper, we show that this assumption is essential, i.e. we provide an example of a complete quasimetric space and a contraction map acting in it whose graph is not closed and which is fixed-point-free. We also describe some geometric properties of such spaces.
[1] A. V. Arutyunov, A. V. Greshnov, “Theory of $(q_1, q_2)$-quasimetric spaces and coincidence points”, Doklady Mathematics, 94:1 (2016), 434–437 | DOI | MR | Zbl
