Browder-Petryshyn 型的严格伪压缩映射的粘滞迭代逼近方法

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．

Viscosity approximation methods for strictly pseudocontractive mappings of Browder-petryshyn type

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).