A Note on Approximating Fixed Points of Pseudocontractive Mappings
Yong Yao · Journal of Mathematical Research and Exposition · 2008
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 {λ_n}(0,1/2]be a sequence satisfying the conditions:(i)lim_(n→∞)λ_n=0;(ii)∑_n=0~∞λ_n=∞.Let the sequence {x_n} be generated from arbitrary x_1∈K by x_(n+1)=(1-λ_n)x_n+λ_nTx_n-λ_n(x_n-x_1),n≥1.Suppose lim_(n→∞)‖x_n- Tx_n‖=0.Then {x_n} converges strongly to a fixed point of T.