非扩张映像不动点的一种变形迭代算法

Algorithm of the modified iterative process for nonexpansive mappings.

在Hilbert空间的框架下,用一种变形的迭代格式xn+1=αnf(xn)+βnxn+γnTxn,研究一闭凸集合C上的非扩张映像的不动点问题,当满足适当的条件,且n→∞时,{xn}强收敛至T的一个不动点,并且此点也是某变分不等式的解.去掉了一些作者提出的相应条件,其结果改进了相应文献的一些近代结果.

It is introduced that a algorithm of the iterative process for nonexpansive mappings on a closed convex subset of a Hilbert space H, where x0 ∈C is arbitrary and xn＋1=αnf（xn）＋βnxn＋γnTxn. for n≥1. It is shown that in certain appropriate conditions, when n→∞, then {xn } converge strongly to a fixed point of T, which is the solution to a variational inequality. The results have improved some recent results.