迭代算法逼近严格伪压缩映象最小范数不动点与变分不等式解

An Iterative Algorithm for Minimum-norm Fixed Points of Strict Pseudo-contraction and Solutions to a Variational Inequality

在Hilbert空间中使用迭代格式xn+1=(1-αn)(δTxn+(1-δ)xn),n≥0来研究严格伪压缩映象T的最小范数不动点问题,采用新方法证明当参数满足适当条件时,序列x{n}强收敛至严格伪压缩映象T的最小范数不动点,同时该不动点也是某变分不等式的解.其结果推广与改进了一些近代相关结果.

In this paper,we deal with an iterative algorithm for solving the minimum-norm fixed point problems of strict pseudo-contraction in Hilbert spaces by xn＋1 =（1-αn）（δTxn ＋（1-δ）xn）,where T：C →Cis a k-strict pseudo-contraction.Under certain approximate conditions,the sequence x{n}converges strongly to the minimum-norm fixed point of strict pseudo-contraction T,which is also a solution to a variational inequality.The results here extend and improve some recent related results.