Geodesic
Coincidence preservation for a one-parameter family of pairs of Zamfirescu-type multi-valued mappings
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2021), pp. 28-34 
Yu. N. Zakharyan; T. N. Fomenko. Coincidence preservation for a one-parameter family of pairs of Zamfirescu-type multi-valued mappings. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2021), pp. 28-34. http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a4/
@article{VMUMM_2021_1_a4,
     author = {Yu. N. Zakharyan and T. N. Fomenko},
     title = {Coincidence preservation for a one-parameter family of pairs of {Zamfirescu-type} multi-valued mappings},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {28--34},
     year = {2021},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a4/}
}
TY  - JOUR
AU  - Yu. N. Zakharyan
AU  - T. N. Fomenko
TI  - Coincidence preservation for a one-parameter family of pairs of Zamfirescu-type multi-valued mappings
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2021
SP  - 28
EP  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a4/
LA  - ru
ID  - VMUMM_2021_1_a4
ER  - 
%0 Journal Article
%A Yu. N. Zakharyan
%A T. N. Fomenko
%T Coincidence preservation for a one-parameter family of pairs of Zamfirescu-type multi-valued mappings
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2021
%P 28-34
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a4/
%G ru
%F VMUMM_2021_1_a4

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

Recently, a concept of a pair of multi-valued Zamfirescu type mappings between metric spaces was introduced by the authors. As well, a coincidence existence theorem was proved for such pairs of mappings. It was shown that this theorem is a generalization of the fixed point theorem for a multi-valued Zamfirescu mapping by Kritsana Neammanee and Annop Kaevkhao (2010). In this paper, the main result is the theorem on the preservation of coincidence point existence in some open set, for a parametrized family of pairs of multi-valued Zamfirescu type mappings. It is shown that this result follows from the theorem on the preservation of zero existence, for a family of $(\alpha,\beta)$-search functionals introduced earlier by T. N. Fomenko. In addition the connection of this result with the theorem by Granas and Frigon (1994) on the preservation of fixed point existence, for a contracting family of multi-valued mappings, is considered.

[1] Zamfirescu T., “Fixed point theorems in metric spaces”, Arch. Math. (Basel), 23 (1972), 292–298

[2] Neammanee K., Kaevkhao A., “Fixed point theorems of multi-valued Zamfirescu mappings”, J. Math. Res., 2:2 (2010), 150–156

[3] Zakharyan Yu.N., Fomenko T.N., “O tochkakh sovpadeniya dlya pary mnogoznachnykh otobrazhenii tipa Zamfiresku”, Vestn. Mosk. un-ta. Matem. Mekhan., 2020, no. 6, 26–33

[4] Fomenko T.N., “Approximation of coincidence points and common fixed points of a collection of mappings of metric spaces”, Math. Notes, 86:1 (2009), 107–120

[5] Fomenko T. N., “Cascade search of the coincidence set of collections of multivalued mappings”, Math. Notes, 86:1–2 (2009), 276–281

[6] Fomenko T.N., “Cascade search principle and its applications to the coincidence problem of $n$ one-valued or multi-valued mappings”, Topol. and its Appl., 157 (2010), 760–773

[7] Fomenko T.N., “Functionals strictly subjected to convergent series and search for singularities of mappings”, J. Fixed Point Theory and Appl., 14 (2013), 21–40 | DOI

[8] Zakharyan Yu.N., Fomenko T.N., “Sokhranenie suschestvovaniya nulei u semeistva mnogoznachnykh funktsionalov i nekotorye sledstviya”, Matem. zametki, 108:6 (2020), 837–850

[9] Frigon M., Granas A., “Resultats du type de Leray–Schauder pour des contractions multivoques”, Topol. Methods Nonlinear Anal., 4 (1994), 197–208

[10] Frigon M., “On continuation methods for contractive and nonexpansive mappings”, Recent Advances on Metric Fixed Point Theory, 48, ed. T. Dominguez Benavides, University of Seville, Seville, Spain, 1996, 19–30