Fixed Point Solutions of Variational Inequalities for Asymptotically Nonexpansive Mappings
Changsong Hu · Mathematica Applicata · 2007
Let X be a real Banach space with a uniformly Gateaux differentiable norm and which possesses uniform normal structure,C a nonempty bounded convex subset of X,T an asymptotically nonexpansive mapping on C and f be a contraction on C.Consider also the iteration processx0∈C,xn+1=αnTnxn+(1-αn)f(xn),n=0,1,2,…,where 0αn1,then it is shown that {xn} and,under certain appropriate conditions on {αn},{xn} converge strongly to a fixed point of T which solves some variational inequality.