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

被引：0
作者：
Lili Chen
Ni Yang
Yanfeng Zhao
Zhenhua Ma
机构：
[1] Shandong University of Science and Technology,College of Mathematics and Systems Science
[2] Harbin University of Science and Technology,Department of Mathematics
[3] Hebei University of Architecture,School of Science
来源：
Journal of Fixed Point Theory and Applications | 2020年 / 22卷
关键词：
Graphical convex metric spaces; Mann iterative scheme; Agrawal iterative scheme; set-valued mappings; fixed point; Primary 47H09; Secondary 47H10;
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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 of T-Mann sequences and T-Agrawal sequences. Furthermore, by using the iterative techniques and graph theory, we investigate the existence and uniqueness of fixed points for set-valued G-contractions in a graphical convex metric space. Moreover, we present some notions of well-posedness and G-Mann stability of the fixed point problems in the above space. Additionally, as an application of our main results, we discuss the well-posedness and G-Mann stability of the fixed point problems for set-valued G-contractions in a graphical convex metric space.
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