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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 2, Pages 72–77 (Mi faa3468)  

Brief communications

Periodic Trajectories and Coincidence Points of Tuples of Set-Valued Maps

B. D. Gel'manab

a Voronezh State University, Voronezh, Russia
b RUDN University, Moscow, Russia

Abstract: A fixed-point theorem is proved for a finite composition of set-valued Lipschitz maps such that the product of their Lipschitz constants is less than 1. The notion of a Lipschitz tuple of (finitely many) set-valued maps is introduced; it is proved that such a tuple has a periodic trajectory, which determines a fixed point of the given composition of set-valued Lipschitz maps. This result is applied to study the coincidence points of a pair of tuples (Lipschitz and covering).

Keywords: set-valued map, Hausdorff metric, Lipschitz set-valued map, fixed point, surjective operator.

Funding Agency Grant Number
Russian Science Foundation 17-11-01168
This work was financially supported by the Russian Science Foundation (project no. 17-11-01168).


DOI: https://doi.org/10.4213/faa3468

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English version:
Functional Analysis and Its Applications, 2018, 52:2, 139–143

Bibliographic databases:

UDC: 517.988.6
Received: 14.04.2017
Accepted:26.05.2017

Citation: B. D. Gel'man, “Periodic Trajectories and Coincidence Points of Tuples of Set-Valued Maps”, Funktsional. Anal. i Prilozhen., 52:2 (2018), 72–77; Funct. Anal. Appl., 52:2 (2018), 139–143

Citation in format AMSBIB
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\pages 72--77
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