无穷个增生映射和的半隐式算法、Ergodic收敛及Curvature系统（英文）  

Semi-Implicit Algorithm for the Sum of Infinite Accretive Mappings,Ergodic Convergence and Curvature Systems

作　　者：魏利[1] 段丽凌[1] 郑雅琴[2] 

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061 [2]河北农业大学理学院,河北保定071001

出　　处：《应用数学》2017年第3期665-676,共12页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11071053);Natural Science Foundation of Hebei Province(A2014207010);Key Project of Science and Research of Hebei Educational Department(ZD2016024);Key Project of Science and Research of Hebei University of Economics and Business(2016KYZ07);the third author is supported by Science and Technology Foundation of Agricultural University of Hebei(LG201612)

摘　　要：在实一致凸且q一致光滑Banach空间中,构造无穷个m增生映射和μ_i逆强增生映射和的公共零点的半隐式迭代算法.证明ergodic收敛性.与近期研究成果相比,限定条件更弱.此外,还研究了一类curvature系统并证明其解恰好是无穷个m增生映射和μ_i逆强增生映射和的公共零点,进而验证了迭代算法的有效性.A semi-implicit iterative algorithm is constructed for the common zeros of the sum of infinite m-accretive mappings and infinite μi-inversely strongly accretive mappings in a real uniformly convex and q-uniformly smooth Banach space. The ergodic convergence is proved under weaker restrictions compared to some of the recent corresponding works. A kind of curvature system is studied in order to show that its solution is just the common zeros of the sum of infinite m-accretive mappings and infinite μi-inversely strongly accretive mappings, which further shows the validity of the iterative algorithm.

关 键 词：m-增生映射 μi逆强增生映射 压缩映射 Ergodic收敛 Curvature系统 

分 类 号：O177.91[理学—数学]