L_p空间的Lipschitz强伪压缩映象的不动点的迭代逼近

Appro Ximation of Fixed Points of Strognly Pseudocontractive Mappings in Lp Spaces

:设X=L_p,P≥2,K是X的非空、闭、凸、有界子集,T:K→K,Lipschitz强伪压缩映象,{a_n}_(n=1)~∞{b_n}_(n=1)~∞{c_n}_(n=1)~∞及{a_n^1}_(n=1)~∞{b_n^1}_(n=1)~∞{c_n^1}_(n=1)~∞为[0,1]中的实数列且满足一定条件,则带误差的Ishikawa迭代序列{X_n}_(n=1)~∞强收敛于T的唯一不动点。

Let X = Lp (or 1p), p≥2, and K be a nonempty closed convex bounded subset of X. suppose T:K→K is a Lipschitxian strictly pseudo-contractive mapping of K into itself. It is proved that Ishikawa iteration process with errors converges srtongly to the unique point of T.