The contraction principle for mappings on a metric space with a graph

被引：4
|
作者：
Jachymski, Jacek [1 ]
机构：
[1] Tech Univ Lodz, Inst Math, PL-93005 Lodz, Poland
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 04期
关键词：
fixed point; Picard operator; partial order; connected graph; Bernstein operator;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give some generalizations of the Banach Contraction Principle to mappings on a metric space endowed with a graph. This extends and subsumes many recent results of other authors which were obtained for mappings on a partially ordered metric space. As an application, we present a theorem on the convergence of successive approximations for some linear operators on a Banach space. In particular, the last result easily yields the Kelisky-Rivlin theorem on iterates of the Bernstein operators on the space C[0, 1].
引用
收藏
页码：1359 / 1373
页数：15
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