An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application

被引:1
|
作者
Sultana, Asrifa [1 ]
Vetrivel, V. [1 ]
机构
[1] Indian Inst Technol Madras, Dept Math, Madras 600036, Tamil Nadu, India
关键词
Bernstein operators; fixed Point; graph; metric space; set-valued mapping; 47H04; 47H10; 54H25; FIXED-POINT THEOREMS;
D O I
10.1080/01630563.2017.1311346
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky-Rivlin theorem on iterates of the Bernstein operators on C[0,1].
引用
收藏
页码:1060 / 1068
页数:9
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