q-一致光滑和严格凸的Banach空间中的无穷个严格伪压缩映射的混合迭代算法  

A General Composite Iterative Algorithm for an Infinite Family of Strictly Pseudo-Contractive Mappings in q-Uniformly Smooth and Strictly Convex Banach Spaces

作　　者：文萌[1] 胡长松[2] 彭济根[1] 

机构地区：[1]西安交通大学数学与统计学院,西安710049 [2]湖北师范学院数学系,湖北黄石435002

出　　处：《数学年刊（A辑）》2014年第4期485-500,共16页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11131006;No.60970149);陕西省教育厅科研计划项目(No.2013JK0591)的资助

摘　　要：在q-一致光滑和严格凸的Banach空间中,研究了无穷个严格伪压缩映射的混合迭代算法,证明了由这种新的算法产生的序列强收敛于这无穷个严格伪压缩映射的公共不动点,并且是变分不等式〈(I-A)x,J_q(p-x)〉≤0,p∈(n i=l)F(T_i)的解.论文推广和改进了一些前人的相应结论.The authors consider a general composite iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in q-uniformly smooth and strictly convex Banach spaces. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of fixed points, which solves the variational inequality 〈（I-A）x,J_q（p-x）〉≤0,p∈（n i=l）F（T_i）. The results improve and extend the i=1 corresponding ones announced by some others.

关 键 词：投影 严格伪压缩映射 不动点 κ-李普希兹 η-强单调 

分 类 号：O177.91[理学—数学]