Viscosity approximation methods for strictly pseudocontractive mappings of Browder-petryshyn type
Browder-Petryshyn 型的严格伪压缩映射的粘滞迭代逼近方法

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).