TY - JOUR
A2 - Yao, Yonghong
AU - Yu, Youli
PY - 2012
DA - 2011/11/03
TI - An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings
SP - 341953
VL - 2012
AB - Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let f:K→K a contractive mapping and T:K→K be a uniformly continuous pseudocontractive mapping with F(T)≠∅. Let {λn}⊂(0,1/2) be a sequence satisfying the following conditions: (i) limn→∞λn=0; (ii) ∑n=0∞λn=∞. Define the sequence {xn} in K by x0∈K, xn+1=λnf(xn)+(1−2λn)xn+λnTxn, for all n≥0. Under some appropriate assumptions, we prove that the sequence {xn} converges strongly to a fixed point p∈F(T) which is the unique solution of the following variational inequality: 〈f(p)−p,j(z−p)〉≤0, for all z∈F(T).
SN - 1110-757X
UR - https://doi.org/10.1155/2012/341953
DO - 10.1155/2012/341953
JF - Journal of Applied Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -