Browder-Petryshyn型的严格伪压缩映射的粘滞迭代逼近方法  

VISCOSITY APPROXIMATION METHODS FOR STRICTLY PSEUDOCONTRACTIVE MAPPINGS OF BROWDER-PETRYSHYN TYPE

作　　者：陈汝栋[1] 宋义生[1] 

机构地区：[1]天津工业大学数学研究所数学系,天津300160

出　　处：《系统科学与数学》2006年第6期651-657,共7页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助课题(10471003;10271001).

摘　　要：主要研究Browder-Petryshyn型的严格伪压缩映射的粘滞迭代逼近过程,证明了Browder-Petryshyn型的严格伪压缩映射的不动点集F(T)是闭凸集．在q-一致光滑且一致凸的Banach空间中,对于严格伪压缩映射T,利用徐洪坤在2004年引进的粘滞迭代得到的序列弱收敛于T的某个不动点．同时证明了Hilbert空间中Browder-Petryshyn型的严格伪压缩映射的相应迭代序列强收敛到T的某个不动点,其结果推广与改进了徐洪坤2004年的相应结果．In this paper, we study viscosity approximation process for strictly pseudo-contractive mapping T of Browder-Petryshyn type and prove that the fixed point set F（T） is a closed convex subset. We obtain a weak convergence theorem of strictly pseudocontractive self-mapping T of a closed convex subset K of a q-uniformly smooth Banach space which is also uniformly convex using viscosity approximation process {xt}, where xt = tf（xt） ＋ （1 - t）Txt, f is an L-Lipschitz strongly pseudocontractive maping. We also prove that {xt} strongly converge to a fixed point of T which solves some variational inequality in Hilbert space. The results extend and improve the corresponding results of Xu Hongkun（2004）.

关 键 词：严格伪压缩映射 粘滞迭代方法 不动点 闭凸集 

分 类 号：O177[理学—数学]