拟非扩张算子序列Ishikawa迭代过程的构造及收敛性

The Construction and Convergence of Ishikawa Iteration for Quasi-Nonexpansive Operator Sequence

对一致凸Banach空间的有界闭凸集上的拟非扩张算子的不动点问题进行了研究。得出了该类算子有公共不动点的充分条件 ,并构造了相应的Ishikawa迭代序列使之收剑于其公共不动点。

A study is made on the fixed points of the quasi nonexpansive operator sequence with a mapping from the bounded closed convex subset of a uniformly convex Banach space into the closed convex subset in the same space. The sufficient conditions for the quasi nonexpansive operator sequence to have a common fixed point are obtained, and the corresponding Ishikawa iterative sequence converging on the common fixed point is constructed. The results obtained in this paper are the extension of the conclusions in the recent publication of the author.