学术
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=anT^mXn＋（1-an）f（xn），n=0，1，2，…，当an∈（O，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．[著者文摘]
文章出处:
《应用数学》-2007年20卷3期 -609-613页
分 类 号:
文献标识码:
A
文章编号:
1001-9847（2007）03-0609-05
Fixed Point Solutions of Variational Inequalities for Asymptotically Nonexpansive Mappings
HU Chang-song （Department of Mathematics, Hubei Normal University, Huangshi 435002, China）
Abstract:
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.[著者文摘]
Key words:
Asymptotically nonexpansive mapping; Strong convergence; Banach limitsIteration
基金资助:
湖北省教育厅重点科研项目（D20052201）
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