Geodesic
Coincidence Points and Generalized Coincidence Points of Two Set-Valued Mappings
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 308 (2020), pp. 42-49

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

We consider set-valued mappings acting in metric spaces and show that, under natural general assumptions, the set of coincidence points of two such mappings one of which is covering and the other is Lipschitz continuous is dense in the set of generalized coincidence points of these mappings. We use this result to study the coincidence points and generalized coincidence points of a set-valued covering mapping and a set-valued Lipschitz mapping that depend on a parameter. In particular, we obtain conditions that guarantee the existence of a coincidence point for all values of the parameter under the assumption that a coincidence point exists for one value of the parameter.
Keywords: coincidence point, generalized coincidence point, covering set-valued mapping. 
@article{TM_2020_308_a2,
     author = {A. V. Arutyunov and E. S. Zhukovskiy and S. E. Zhukovskiy},
     title = {Coincidence {Points} and {Generalized} {Coincidence} {Points} of {Two} {Set-Valued} {Mappings}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {42--49},
     publisher = {mathdoc},
     volume = {308},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_308_a2/}
}
TY  - JOUR
AU  - A. V. Arutyunov
AU  - E. S. Zhukovskiy
AU  - S. E. Zhukovskiy
TI  - Coincidence Points and Generalized Coincidence Points of Two Set-Valued Mappings
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2020
SP  - 42
EP  - 49
VL  - 308
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2020_308_a2/
LA  - ru
ID  - TM_2020_308_a2
ER  - 
%0 Journal Article
%A A. V. Arutyunov
%A E. S. Zhukovskiy
%A S. E. Zhukovskiy
%T Coincidence Points and Generalized Coincidence Points of Two Set-Valued Mappings
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2020
%P 42-49
%V 308
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2020_308_a2/
%G ru
%F TM_2020_308_a2
A. V. Arutyunov; E. S. Zhukovskiy; S. E. Zhukovskiy. Coincidence Points and Generalized Coincidence Points of Two Set-Valued Mappings. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 308 (2020), pp. 42-49. http://geodesic.mathdoc.fr/item/TM_2020_308_a2/