Banach空间中Lipschitz伪压缩映射的近似不动点序列及其收敛定理

研究了Lipschitz伪压缩映射的黏滞迭代方法.设E为一致光滑Bannach空间,K为E的闭凸子集,TK→K为Lipschitz伪压缩映射且其不动点集F(T)非空,f为K上的压缩映射且t∈(0,1).若黏滞迭代路径{xt},xt=(1-t)f(xt) tTxt且对任意初始向量x1∈K,迭代序列{xn}定义为xn 1=λnθnf(xn) 1-λn(1 θn)]xn λnTxn,则当t→1-和n→∞时,{xt}和{xn}都强收敛于T的不动点,同时该不动点还是一类变分不等式的解.

Approximate Fixed Point Sequences and Convergence Theorems for Lipschitz Pseudocontractive Mappings in Banach Spaces

In this article,viscosity approximation methods for Lipschitz pseudocontractive mappings are studied. Consider a Lipschitz pseudocontractive self-mapping T of a closed convex subset K of a Banach space E. Suppose that the set F(T) of fixed points of T is nonempty. For a contraction f on K and t ∈ (0,1),let {xt} be defined by xt = (1 - t)f(xt) + tTxt,and for any fixed element x1 ∈ K,let the iteration process {xn} be defined by xn+1 := λnθnf(xn) + 1 - λn(1 + θn)]xn + λnTxn. If E is a uniformly smooth Banach space,then it is shown that both {xt} and {xn} converges strongly to a fixed point of T which solves some variational inequality.