双曲空间中渐近非扩张型映射混合SP-迭代算法的收敛性  

Convergence of mixed type SP-iterative scheme of asymptotically nonexpansive type mappings in hyperbolic spaces

作　　者：刘涌泉 方达 黄星 LIU Yongquan;FANG Da;HUANG Xing(School of Digital Media,Ji′an Preschool Teachers College,Ji′an 343000,China;School of Sciences,Changzhou Institute of Technology,Changzhou 213032,China)

机构地区：[1]吉安幼儿师范高等专科学校数字传媒学院,江西吉安343000 [2]常州工学院理学院,江苏常州213032

出　　处：《高师理科学刊》2025年第1期1-12,共12页Journal of Science of Teachers'College and University

基　　金：江西省教育厅科学技术研究项目(GJJ2410701);常州工学院2023年度教学建设项目(JGKT2023-11)。

摘　　要：在双曲空间中,引入关于多个渐近拟非扩张映射以及多个几乎渐近拟非扩张映射新的混合SP-迭代算法,获得了多个渐近拟非扩张映射以及多个几乎渐近拟非扩张映射在新的混合SP-迭代算法下一些重要结论,利用这些结论进一步获得了多个渐近非扩张映射以及多个几乎渐近非扩张映射在新的混合SP-迭代算法下的Δ-收敛性定理,并在这些映射具有半紧的条件下,证明了相应的混合SP-迭代算法强收敛到这些映射的公共不动点.所得结果推广和改进了一些相关文献的结论.A new mixed type SP-iterative scheme for some asymptotically quasi-nonexpansive mappings and some nearly asymptotically quasi-nonexpansive mappings is introduced in hyperbolic spaces.Some important conclusions regarding some asymptotically quasi-nonexpansive mappings and some nearly asymptotically quasi-nonexpansive mappings under the new SP-iteration scheme are obtained.By using these conclusions,theΔ-convergence theorem for some asymptotically nonexpansive mappings and some nearly asymptotically nonexpansive mappings under the new mixed type SP-iterative algorithm are established.Moreover,it is proved that the corresponding mixed type SP-iterative algorithm strongly converges to the common fixed point of these mappings under the condition that these mappings are semi-compact.The obtained results have improve and extend the conclusions of some relevant literature.

关 键 词：公共不动点 双曲空间 几乎渐近拟非扩张映射 SP-迭代算法 

分 类 号：O177.91[理学—数学]