Banach空间中非扩张映像的一般正则化方法

General Regularization Methods for Nonexpansive Mappings in Banach Spaces

研究了一致光滑的Banach空间中非扩张映像的一般正则化方法.利用Hilbert空间中的正则化方法迭代格式和一致光滑Banach空间中的基本结论,在非扩张映像T不动点集Fix(T)非空的条件下,证明了在Banach空间中,一般正则化方法强收敛到非扩张映像的T唯一不动点.最后,通过改变算法的迭代格式,在条件更弱的条件下,证明了算法的强收敛性.此类正则化算法可以解决管理科学、医学图像处理中的一类变分不等式问题.

The general regularization method for nonexpansive mappings Tin the uniformly smooth Banach space was investigated.According to the iterative algorithm for regularization method in the Hilbert space and the basic conclusion of the uniformly smooth Banach space,on condition that the set Fix（T）of fixed points of Tis nonempty,the algorithm converge to a fixed point of non-expansive mappings Tstrongly in the Banach space.Finally,the algorithm generates a strong convergence sequence when the iterative algorithm is changed under less restrictive assumptions.The general regularization method is robust and flexible in some variational inequalities problems of management science and medical image processing.