一致凸Banach空间Ishikawa迭代序列收敛性

Convergence of Ishikawa iterative sequences in uniformly convex Banach spaces

利用一致凸Banach空间中凸性模的大小与其特征不等式的等价关系 ,即当 p≥ 2时 ,Banach空间X是一致凸的 ,并且 ,当且仅当X中的范数满足不等式‖ (1-t)x +ty‖ p+cw(t)‖x - y‖ p≤ (1-t)‖x‖ p+t‖y‖ p 时 ,其凸性模δX(ε)≥cεp(0 <ε <2 ,0 <c <1,p≥ 2 ) , x ,y∈X ,其中t∈ (0 ,1) ,w (t) =t(1-t) p+(1-t)tp.研究了非线性算子关于由Ishikawa迭代序列的收敛性 。

Employing the relationship of equivalence between module of convex and characteristic inequality in uniformly convex Banach spaces, i.e., Banach space X is uniformly convex and its module of convex (δX(ε)≥)cε~p (0<ε<2,0<c<1,p≥2) if and only if norm of X is satisfied with the inequality ‖(1-(t)x+)ty‖~p+cw(t)‖x-y‖~p≤(1-t)‖x‖~p+t‖y‖~p, x,y∈X, and t∈(0,1), w(t)=(t(1-)t)~p+(1-t)t^p, the authors obtained the convergence of Ishikawa iterative sequences for nonlinear operator. The main results spread the other corresponding conclusions.