Strong Convergence to Cesro Means for Non-expansive Mappings in Banach Spaces
Ping Zuo · Journal of Nanchang University · 2010
Let f be a fixed contraction with contractive constant h and T be a non-expansive mapping with F(T)≠Φ.The sequence {xn} is iteratively defined as follows. xn+1=αn f(xn)+(1-αn)1/n+1 sum Tjxn from j=0 to n,n∈N,where {αn}(0,1) satisfies the conditions lim αn = 0 n→∞and sum αn=∞ from n=1 to ∞.It proves that {xn } converges strongly to the unique solution x~ to some variational inequality in F(T).Our results improve the main results in Xu,Shimizu-Takahashi and Shioji-Takahashi.