关于k-严格伪非扩展映象的不动点问题

On Fixed Point Problem of k-strictly Pseudononspreading Mapping

介绍了一类新的k-严格伪非扩展映象,举例说明了该类映象的存在性,并在Hilbert空间中建立严格伪扩展映象的不动点与变分不等式问题解集的等价关系.利用该等价关系和求解变分不等式问题的投影技巧、预解算子技巧和松弛迭代等方法,可以研究逼近k-严格伪非扩展映象不动点的数值方法.

This paper introduces a class of new κ-strictly pseudononspreading mappings with some examples in Hilbert space.Equivalence between the fixed point problem of strictly pseudononspreading mapping and variational inequality is established.This alternative equivalent formulation can be used to analyze some numerical methods for finding a fixed point of pseudononspreading mapping based on the current technique such as projection,resolvent operator and relaxed iteration.