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.
出处
《应用数学》
CSCD
北大核心
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)
关键词
渐近非扩张映射
压缩映射
BANACH极限
Asymptotically nonexpansive mapping
Strong convergence
Banach limitsIteration
