b-凸度量空间的不动点理论  

Fixed Point Theory in b-convex Metric Spaces

作　　者：李朝博 陈丽丽[1] LI Chao-bo;CHEN Li-li(Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China)

机构地区：[1]哈尔滨理工大学应用数学系,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2021年第2期143-148,共6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：b-度量空间是一类广义的度量空间,近年来引起了国内外学者的广泛关注。首先在b-度量空间中引入凸结构,从而给出b-凸度量空间的概念,并在该空间中给出了Mann迭代算法。进一步利用Mann迭代所生成的序列,证明了在一定条件下,压缩映射在完备的b-凸度量空间中存在唯一的不动点。b-metric spaces are a kind of generalized metric spaces,which have attracted extensive attention of scholars at home and abroad in recent years.In this paper,the convex structure is firstly introduced in b-metric spaces,and consequently the notion of the convex b-metric space is shown.Moreover,Mann iteration is proposed in above space.Furthermore,by utilizing the sequence which is generated by Mann iteration,under some conditions,it is proved that contractive mappings have the unique fixed point in the complete convex b-metric spaces respectively.

关 键 词：b-度量空间 凸结构 MANN迭代 

分 类 号：O177.2[理学—数学]