渐近非扩张映射变分不等式的不动点解  

Fixed Point Solutions of Variational Inequalities for Asymptotically Nonexpansive Mappings

作　　者：胡长松[1] 

机构地区：[1]湖北师范学院数学系,湖北黄石435002

出　　处：《应用数学》2007年第3期609-613,共5页Mathematica Applicata

基　　金：湖北省教育厅重点科研项目(D20052201)

摘　　要：设X是实的Banach空间且有一致Gateaux可微范数和一致正规结构,C是X的非空闭凸子集,T,f分别是C上的渐近非扩张映射与压缩映射,x0∈C,xn+1=αnTnxn+(1-αn)f(xn),n=0,1,2,…,当αn∈(0,1)满足适当条件时,则{xn}强收敛到某变分不等式的不动点解.Let X be a real Banach space with a uniformly Gateaux differentiable norm and which possesses uniform normal structure, C a nonempty bounded convex subset of X,Tan asymptotically nonexpansive mapping on C and f be a contraction on C. Consider also the it- eration process xo∈ C,xn＋1 = anT^nxn＋（1-an）f（xn）,n = 0,1,2,…, where0〈an〈1; then it is shown that {xn} and,under certain appropriate conditions on {an }, {xn } converge strongly to a fixed point of T which solves some variational inequality.

关 键 词：渐近非扩张映射 压缩映射 BANACH极限 

分 类 号：O177.91[理学—数学]