改进的Mann迭代序列在Banach空间中相对非扩张多值映射下的强弱收敛性

Weak and Strong Convergence Theorems by Modified Mann Iterations for Relatively Nonexpansive Multi-valued Mapping in Banach Spaces

对于多值相对非扩张映射引入了一种新的迭代序列,并证明了在一致凸、一致光滑的Banach空间中该序列的广义投影强收敛于多值相对非扩张映射的一不动点,进一步证明了该序列在适当条件下的强、弱收敛性.

A new iterative sequence was introduced and proved that the generalized projection of iteration sequence strongly convergences to fixed point of relatively nonexpansive multi-valued mapping in uniformly smoothly and uniformly convex in Banach space.The weak and strong convergence theorems for relatively nonexpansive multl-valued mappings were proved in some conditions.