迭代逼近m-增生映象的零点  

Approximation of the Iterative Method for a Zero of m-Accretive Mappings

作　　者：黄建锋[1] 王元恒[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,金华321004

出　　处：《数学学报（中文版）》2008年第3期435-446,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助课题(10471113)

摘　　要：设E是具有一致正规结构的实Banach空间,其范数是一致Gateaux可微的.设A是m-增生映象,使得C=■是E的凸子集,数列{α_n)■[0,1],{r_n}■ (0,∞),在适当的条件下,则由(1.2)式定义的迭代序列{x_n}强收敛于A^(-1)(0)中的点.其次证明了:设E是一致凸Banach空间,其范数是Frechet可微的.设数列{α_n},{β_n)■(0,1),{r_n}■(0,∞),满足适当的条件.如果A^(-1)(0)∩B^(-1)(0)≠φ,则由(3.20)式定义的序列{x_n}弱收敛于A^(-1)(0)∩B^(-1)(0)中的点.其结果推广和改进了Kamimura,Takahashi(2000)的定理2及Xu H.K.(2006)的定理4.1,定理4.2和定理4.3:(i)Kamimura,Takahashi(2000)定理2中的假设"自反Banach空间E的每个有界闭凸子集对非扩张自映象有不动点性质"被去掉;(ii)Xu H.K.(2006)的假设"E是具有弱连续对偶映象J_φ的自反Banach空间",被本文的假设"E是具有一致正规结构且其范数是一致Gateaux可微的Banach空间"所取代.从而补充了Xu H.K.(2006)未包含的另外一些Banach空间.同时还证明了逼近两个m-增生映象的公共零点,其结果也推广和改进了Mainge的相应结果.Suppose E is a Banach space with uniformly normal structure and E also has uniformly Gateaux differentiable norm. Let A be an m-accretive suppose operator such that C = D（A） is a convex subset of E. Let {αn} be a sequence in the interval （0,1） and let {rn} be a sequence in the interval （0,∞）. Then, under some suitable conditions, the sequence {xn} defined by （1.2） converges strongly to an element of A^-1 （0）. Secondly, we also prove that： Let E be a uniformly convex Banach space whose norm is Frechet differentiable. Let {αn}, {βn} be two squences in the interval （0, 1） and let {rn} be a sequence in the interval （0,∞）. If A^-1（0）∩B^-1（0）≠Ф, then, under some suitable conditions, the sequence {xn} defined by （3.20） converges weakly to an element in A^-1 （0）∩B^-1 （0）. Our results extend and improve Theorem 2 of Kamimura, Takahashi （2000） and theorem 4.1, Theorem 4.2, Theorem 4.3 of Xu （2006）： （i） In Theorem 2 of Kamimura, Takahashi （2000）, the condition ＂Every bounded, closed and convex subset of a reflexive Banach space has the fixed point property for nonexpansive mappings＂ is removed; （ii） In Xu H. K. （2006）, the condition ＂E is reflexive and has a weakly continuous duality map Jφ＂ is replaced by ＂E is a Banach space with uniformly normal structure and E also has uniformly Gateaux differentiable norm.＂ so that it contains some Banach spaces besides the Banach space which is in Xu H. K. （2006）. At the same time, we state how to approximate a common zero of two m-accretive operators in E. Hence, the results also improve and unify some corresponding results.

关 键 词：一致正规结构 一致凸空间 M-增生映象 

分 类 号：O177.91[理学—数学]