拟非扩张映像族的不动点的迭代逼近  

Iterative approximation of fixed points for a family of quasi-nonexpansive mappings

作　　者：崔艳兰[1] 杨鹏[1] 宋娜娜[1] 

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《沈阳师范大学学报（自然科学版）》2012年第1期20-22,共3页Journal of Shenyang Normal University:Natural Science Edition

基　　金：陕西省自然科学基金资助项目(2010JQ1005)

摘　　要：近年来,学者们对映像族的不动点的研究越来越活跃,迭代格式也越来越丰富,但大多都是对非扩张映像族的不动点的迭代法进行的研究,而且有很多算法比较繁琐。为了寻求一种更好的算法来逼近拟非扩张影像族的不动点,在实Hilbert空间中引入一种变形的投影迭代格式,用以逼近2个集合的公共点,这2个集合是拟非扩张映像族的不动点的集合。在适当的条件下,利用混杂投影算法证明了拟非扩张影像族的不动点的强收敛定理,这是构造实Hilbert空间中的拟非扩张映像族的不动点的新的迭代算法。新算法不要求映像的次闭性质,而且比最近的算法简单,最重要的是迭代格式具有一般性。这也是迭代算法主要研究的方向,因此,该算法可以成为以后迭代法研究的参考依据。In recent years, the scholars on the fixed point study of quasi-nonexpansive mapping are more and more active, and iterative scheme is also more and more rich, but the algorithm on family of nonexpansive of fixed point iterative scheme are more complicated. In this paper, the purpose is to find a better solution to combine family of quasi-nonexpansive mapping of fixed point. In real Hilbert space an modification of iterative program is introduced to combine the common element of two sets, which are family of quasi-nonexpansive mapping. Under appropriate conditions, and by using new hybrid iteration scheme we prove strong convergence theorem on family of quasi-nonexpansive mapping of fixed point. This is a new iterative algorithm to construct family of quasi-nonexpansive mapping of fixed point without making use of demi-closedness property for mapping T, but it is easier and more general than later. It is also the direction of study on iterative scheme. Therefore, this paper can be a reference for iteration scheme later.

关 键 词：拟非扩张映像族 投影算法 实HILBERT空间 强收敛 

分 类 号：O177.91[理学—数学]