Fixed point theorems for set-valuedG-contractions in a graphical convex metric space with applications

被引：10
|
作者：
Chen, Lili [1 ,2 ]
Yang, Ni [2 ]
Zhao, Yanfeng [1 ]
Ma, Zhenhua [3 ]
机构：
[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
[2] Harbin Univ Sci & Technol, Dept Math, Str Xuefu 52, Harbin 150080, Peoples R China
[3] Hebei Univ Architecture, Sch Sci, Zhangjiakou 075024, Peoples R China
来源：
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2020年 / 22卷 / 04期
关键词：
Graphical convex metric spaces; Mann iterative scheme; Agrawal iterative scheme; set-valued mappings; fixed point; WELL-POSEDNESS; MAPPINGS;
D O I：
10.1007/s11784-020-00828-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we first introduce the concept of graphical convex metric spaces and some basic properties of the underlying spaces. Different from related literature, we generalize Mann iterative scheme and Agrawal iterative scheme for set-valued mappings to above spaces by introducing the concepts ofT-Mann sequences andT-Agrawal sequences. Furthermore, by using the iterative techniques and graph theory, we investigate the existence and uniqueness of fixed points for set-valuedG-contractions in a graphical convex metric space. Moreover, we present some notions of well-posedness andG-Mann stability of the fixed point problems in the above space. Additionally, as an application of our main results, we discuss the well-posedness andG-Mann stability of the fixed point problems for set-valuedG-contractions in a graphical convex metric space.
引用
收藏
页数：23
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