Kantorovich's Fixed Point Theorem and Coincidence Point Theorems for Mappings in Vector Metric Spaces

被引：4
|
作者：
Arutyunov, Aram, V [1 ]
Zhukovskiy, Evgeny S. [1 ,2 ]
Zhukovskiy, Sergey E. [1 ]
Zhukovskaya, Zukhra T. [1 ]
机构：
[1] RAS, VA Trapeznikov Inst Control Sci, Profsoyuznaya St 65, Moscow 117997, Russia
[2] Derzhavin Tambov State Univ, Int Naya Str 33, Tambov 392622, Russia
来源：
SET-VALUED AND VARIATIONAL ANALYSIS | 2022年 / 30卷 / 02期
基金：
俄罗斯基础研究基金会; 俄罗斯科学基金会;
关键词：
Kantorovich's fixed point theorem; Coincidence point; Vector metric space; SET; PRINCIPLE; EQUATIONS;
D O I：
10.1007/s11228-021-00588-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The fixed points and coincidence points of mappings of v-metric spaces, i.e., sets on which a vector metric is defined, are investigated. The values of such a metric are elements of a cone of a Banach space rather than real nonnegative numbers. Analogs of Kantorovich's theorems on the existence and uniqueness of a fixed point and the convergence of an iteration sequence to this point are obtained. Conditions for the existence of a coincidence point of two mappings are obtained. The results obtained are generalized to the case of set-valued mappings.
引用
收藏
页码：397 / 423
页数：27
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