非扩张映像的一类压缩逼近

Contractive Approximations of Nonexpansive Mappings

对Hilbret空间中的非扩张映像建立了一类压缩逼近迭代,并将这一类压缩逼近推广到具有弱连续共轭映像的一致凸Banach空间中。

Let X be a reflxive Banach Space with X~* strictly convex and with a weakly contin uous duality mapping of X into X~*, and T be a nonexpansive mapping of a bounded closed convex subset C of X, then a sequence defined by y_n=T_n^(k(n))y_(n-1) converges strongly to a fixed point of T, where T_n= a_nT, {a_n} and {k(n)} are sequences of positive number that satisfy some conditions.