Let K be a nonempty bounded closed convex subset of a real reflexive Banach space E with a uniformly Gateaux differentiable norm. Let T ： K →K be a uniformly continuous pseudocontractive mapping. Suppose every close...Let K be a nonempty bounded closed convex subset of a real reflexive Banach space E with a uniformly Gateaux differentiable norm. Let T ： K →K be a uniformly continuous pseudocontractive mapping. Suppose every closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Let {λn} C （0,1/2] be a sequence satisfying the conditions： （i） limn→∞λn=0; （ii） ∑n=0^∞ λn=∞. Let the sequence {xn} be generated from arbitrary x1∈K by xn＋1 = （1 -λn）xn ＋ λnTxn -λn（xn - x1）, n ≥ 1. Suppose limn→∞‖xn - Txn‖ = 0. Then {xn} converges strongly to a fixed point of T.展开更多
基金the National Natural Science Foundation of China （No. 10771050）.
文摘Let K be a nonempty bounded closed convex subset of a real reflexive Banach space E with a uniformly Gateaux differentiable norm. Let T ： K →K be a uniformly continuous pseudocontractive mapping. Suppose every closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Let {λn} C （0,1/2] be a sequence satisfying the conditions： （i） limn→∞λn=0; （ii） ∑n=0^∞ λn=∞. Let the sequence {xn} be generated from arbitrary x1∈K by xn＋1 = （1 -λn）xn ＋ λnTxn -λn（xn - x1）, n ≥ 1. Suppose limn→∞‖xn - Txn‖ = 0. Then {xn} converges strongly to a fixed point of T.
