Locally covering maps in metric spaces and coincidence points

被引：58

作者：

Arutyunov, Aram ^{[1
]}

Avakov, Evgeniy ^{[2
]}

Gel'man, Boris ^{[3
]}

Dmitruk, Andrei ^{[4
]}

Obukhovskii, Valeri ^{[3
]}

机构：

[1] Patrice Lumumba Peoples Friendship Univ, Moscow 117198, Russia

[2] RAS, Control Problems Inst, Moscow 117806, Russia

[3] Voronezh State Univ, Voronezh 394006, Russia

[4] RAS, Cent Econ & Math Inst, Moscow 117418, Russia

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2009年 / 5卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

alpha-covering map; locally covering map; coincidence point; fixed point; contraction map; multivalued map; control system; REGULARITY; MAPPINGS;

D O I：

10.1007/s11784-008-0096-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the notion of alpha-covering map with respect to certain subsets in metric spaces. Generalizing results from [1] we use this notion to give some coincidence theorems for pairs of single-valued and multivalued maps one of which is relatively alpha-covering while the other satisfies the Lipschitz condition. These assertions extend some classical contraction map principles. We define the notion of alpha-covering multimap at a point and give conditions under which the covering property of a multimap at each interior point of a set implies that it is covering on the whole set. As applications we consider the solvability of a system of inclusions and the existence of a positive trajectory for a semilinear feedback control system.

引用

页码：105 / 127

页数：23

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