论文标题
关于Krasnosel'ski \Vı-Mann迭代的稳定性
On the Stability of Krasnosel'ski\vı-Mann Iterations
论文作者
论文摘要
首先，我们调用了涉及非专业运算符的翻译基本方法的弱收敛（分别强烈收敛），以建立与扰动和近似值相关方法的弱收敛性（分别强烈收敛）。然后，我们采用上述结果的技术来扩展来自经典的krasnosel'ski \vı-mann迭代的收敛结果，以找到其放松变体，以找到相关的非Xansive operators的常见固定点。最后，我们展示了用于解决单调包含问题的广义近端算法的应用。
Firstly, we invoke the weak convergence (resp. strong convergence) of translated basic methods involving nonexpansive operators to establish the weak convergence (resp. strong convergence) of the associated method with both perturbation and approximation. Then we employ the technique obtaining the result above to extend convergence results from the classic Krasnosel'ski\vı-Mann iterations to their relaxation variants for finding a common fixed point of associated nonexpansive operators. At last, we show applications on generalized proximal point algorithms for solving monotone inclusion problems.
