复合Halpern迭代逼近一族m-增生映像公共零点

在严格凸的Banach空间E中，介绍了一种新的复合迭代方法强收敛到一族m-增生映像公共零点。K是E中非空闭凸子集，假定E的每个非空闭凸子集上的非扩张映像都存在不动点，Ai：K→E（i=1，2，…，r）是一族m-增生映像，{xn}是由复合Halpem格式定义的迭代序列，证明了当n→∞时，{xn}强收敛于方程Aix=0（i=1，2，…，r）的公共解，改进和推广了Zegeye和Shahzad等人的相应结果。

Composite Halpern Iteration for Approximating Common Zero of a Finite Family of m-Accretive Mappings

This paper introduces a new composite halpern iteration process for approximating common zero points of m- accretive mappings in Banach spaces. Suppose K is a closed convex subset of a strictly convex real Banach space E which has a uniformly Gateaux differentiable norm. Suppose that every nonempty closed convex bounded subset of E has the fixed point property for nonexpansive mappings. Ai ： K→E（i=1,2, ... ,r）is a family of m-accretive mappings from K to E, {xn} is a sequence defineded by composite Halpern iteration.Then as n→∞, {xn} converges strongly to a common solution of the equations Ai x=0 （i=1,2,..., r）.