零点问题不动点问题和平衡问题的混杂算法

Hybrid Algorithms of Common Elements for Fixed Point Problems,Equilibrium Problems and Zero Point Problems

在具有K-K性质的严格凸的一致光滑Banach空间的框架下,构造了一种新的关于拟φ-非扩张映像的不动点集与极大单调算子的零点集以及一个平衡问题解集的公共元素的混杂投影迭代方法,而且利用所设计之算法证明了其公共元素之强收敛定理。作为应用,给出了寻找一个凸泛函的极小值点问题。

A new hybrid projection method was considered to find common elements of the set of fixed points of a quasi-φ-nonexpansive mapping, the set of solutions of an equilibrium problem and the set of zero points of a maximal monotone operator. A strong convergence theorem of common elements was proved by using new analysis techniques in the setting of strictly convex, and uniformly smooth Banach spaces with the K-K property. As an application, the problem of finding a minimizer of a convex function was considered.