论文标题
在Banach空间中强烈单调映射的强收敛定理
Strong convergence theorems for strongly monotone mappings in Banach spaces
论文作者
论文摘要
让$ e $成为一个均匀的平滑且均匀凸出的真实Banach空间，而$ e^*$是其双空间。假设$ a：e \ rightarrow e^*$是有界的，非常单调并满足范围条件，以至于$ a^{ - 1}（0）\ neq \ emptyset $。受Alber [2]的启发，我们介绍了Lyapunov功能，并使用Banach空间的新几何特性，以显示迭代算法的强收敛到$ ax = 0 $的解决方案。
Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone and satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired by Alber [2], we introduce Lyapunov functions and use the new geometric properties of Banach spaces to show the strong convergence of an iterative algorithm to the solution of $Ax=0$.
