On the Convergence of Ishikawa Iteration Process with Errors for Lipschitzian Strongly Pseudocontractive Mappings in Banach Spaces
Peng Jian-wen · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2006
Let K be a dosed convex subset of an arbitrary real Banach space X,and T:K→K be a Lipschitz strongly pseudo- contractive mapping such that Tx~*=x~* for some x~*∈X.Under the lack of assumption that∑_(n=0)~∞α_nβ_n＜∞,it is shown that the Ishikawa iterative sequence with errors converges strongly to the unique fixed point of T.Moreover,this result provides a general convergence rate estimation for such a sequence.These results unify,improve and generalize the recent correspond- ing results.