Zero Preservation for a Family of Multivalued Functionals, and Applications to the Theory of Fixed Points and Coincidences

被引：5

作者：

Fomenko, T. N. ^{[1
]}

Zakharyan, Yu. N. ^{[2
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Computat Math & Cybernet, Moscow 119991, Russia

[2] Lomonosov Moscow State Univ, Fac Mech & Math, Moscow 119991, Russia

来源：

DOKLADY MATHEMATICS | 2020年 / 102卷 / 01期

关键词：

parametric family of functionals; multivalued mapping; fixed point; coincidence point; Zamfirescu mapping; Zamfirescu-type pair of mappings; preservation of coincidence existence; parametric family of mappings;

D O I：

10.1134/S1064562420040225

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A theorem on the zero existence preservation for a parametric family of multivalued (alpha, beta)-search functionals on an open subset of a metric space is proved. Several corollaries on the existence preservation for preimages of a closed subspace, for coincidence points, and for common fixed points under the action of a parametric family (a number of families) of mappings are obtained. The notion of a Zamfirescu-type pair of mappings is introduced, and a coincidence theorem for such pairs of mappings is obtained. In addition, a theorem on the coincidence existence preservation for a parametric family of such pairs of mappings is obtained. The obtained results imply several well-known theorems.

引用

页码：272 / 275

页数：4

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