Banach空间中3类问题公共解的弱收敛定理

Weak Convergence Theorems for a Common Solution on Three Problems in a Banach Space

在2-一致凸、一致光滑的Banach空间,引入了一个迭代序列来逼近3个集合的公共点,这3个集合分别是平衡问题的解集、变分不等式的解集和相对非扩张映射的不动点集。表明了这一序列弱收敛到这3个集合的公共点。

This paper introduces an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping and the set of solutions of an equilibrium problem in a Banach space. Then the authors show that the sequence converges weakly to a common element of the three sets.