变分不等式问题不动点问题和零点问题的公共元的强收敛定理

Strong convergence theorems of common elements for fixed point zero point problems and variational inequality problems

设Banach空间是一致光滑的和严格凸的并且具有K-K性质,在此空间中设计一种新的收缩投影迭代法去逼近一个极大单调算子的零点集与一个半相对非扩张映像的不动点集以及宽松的协和算子的有限个变分不等式问题解集的公共元,并利用所设计的算法证明了公共元的强收敛定理。

In the strictly convex and uniformly smooth Banach spaces with the K-K property.a new contraction projection iteration method is made to approach common elements of the set of fixed points of a hemi-relatively nonexpansive mappings,the set of zero points of a maximal monotone operator and the set of soultions of finite variational inequalities for relaxed teamwork operators.And the strong convergence theorem of the common element is demonstrated by the designed algorithm.