赋有向图凸度量空间的Mann迭代算法  

Mann Iterative Algorithm in Convex Metric Spaces Endowed with a Directed Graph

作　　者：杨妮 陈丽丽 YANG Ni;CHEN Li-li(School of Applied Sciences, Harbin University of Science and Technology, Harbin 150080, China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2021年第1期139-143,共5页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11401141);黑龙江省高校青年创新人才培养计划(UNPYSCT-2017078);黑龙江省博士后科研启动基金(LBH-Q18067).

摘　　要：赋有向图的度量空间相比于一般的度量空间,在空间结构上更为复杂,有向图本身并不具有线性结构,在探究映射不动点的逼近问题上难度相对较大,从而受到了众多学者的广泛关注。首次通过在该空间中引入凸结构,给出了赋有向图凸度量空间的概念,并在该空间中得到G-单调非扩张映射在Mann迭代下生成序列的收敛性定理,并给出反例说明Mann迭代下生成序列不一定收敛到G-单调非扩张映射的不动点。Compared to the general metric space,the metric space endowed with a directed graph is more complex in space structure,and the directed graph itself does not have a linear structure,and it is relatively difficult to explore the problems of the fixed points of the mappings.In this paper,the convex structure is introduced in the metric space endowed with a directed graph for the first time,and the convex metric spaces endowed with a directed graph is defined.Moreover,the convergence theorem of the sequence which is generated by the Mann iterative algorithm of G-monotone nonexpansive mappings is obtained.Furthermore,an example is given to illustrate that the sequence generated by Mann iteration does not necessarily converge to the fixed point of G-monotone nonexpansive mapping.

关 键 词：赋有向图凸度量空间 凸结构 Mann迭代算法 

分 类 号：O177.2[理学—数学]