复合Halpern迭代逼近可数个增生映像的公共零点

设E是严格凸和自反的实Banach空间且其范数是一致Gateaux可微的，K是E中非空闭凸子集，Ai：K→E（i∈N）是m-增生映像且公共不动点集非空，u∈K是给定点，X1∈K是任一初始点，{αn}^∞ n=1、{β}^∞ n=1是0，1]中的实数列且满足如下条件：（i）lim n→∞αn=0,∑^∞ n=1 αn=∞，∑^∞ n=1｜αn＋1－αn｜〈∞；（ii）lim n→∞βn=0，∑^∞ n=1｜βn＋1－βn｜〈∞。设{Xn}^∞ n=1是由下面复合Halpern格式定义的迭代序列：{yn=βnXn＋（1-βn）SXn,n≥0 Xn＋1=αnu＋（1-αn）yn其中S=∑∞ i=1ξiJAi,JAi=（1＋Ai）^-1（i∈N），那么{Xn}∞ n=1强收敛于{Ai}i∈N的公共0点。本文的结果改进和推广了Zegeye和Shahzad，Ofoedu以及其他作者的相应结果。

Composite Halpern Iteration for Approximating Common Zero of Conntably Infinite Family of m-accretive Mappings

Let K be a closed convex nonempty subset of a strictly convex and real reflexive Banach space E which has a uniformly GCtteaux differentiable norm. Let Ai：K→E（i∈N）be a countably infinite family of m-accretive mappings such that ∩^∞ i=1N（Ai）≠Ф. For arbitrary u,x1∈K, {αn}^∞ n=1 and {βn}^∞ n=1 are real sequences in the 0,1] satisfying the conditions：（i）lim n→∞αn=0,∑^∞ n=1 αn=∞,∑^∞ n=1｜αn＋1-αn｜〈∞;（ii）lim n→∞βn=0,∑^∞ n=1｜βn＋1-βn｜〈∞.{Xn}^∞ n=1 be composite I-Ialpern iteration definited by：{yn=βnXn＋（1-βn）SXn,n≥0 Xn＋1=αnu＋（1-αn）yn Where S=∑∞ i=1ξiJAi,JAi=（1＋Ai）^-1（i∈N）,then,{Xn}^∞ n=1 converges strongly to a common zero of {Ai}i∈N .The results presented in this paper improve and extend the correspoinding ones of Hegeye and Shahzad and Ofoedu and others.