Strong Convergence Theorem of Viscosity Approximation Methods
Shi Qiu · Journal of Civil Aviation University of China · 2010
Let E be a uniformly smooth Banach space,C a nonempty closed convex subset of E.Let f:C →C be a contractive mapping,and T:C→C be a nonexpansive mapping with the set of fixed point F(T)≠0,the initial guess x0∈C is chosen arbitrarily.Under∣ ‖Tzn-xn‖-‖zn-xn‖∣= o(βn),the sequence {xn} defined by xn+1 = αn f(xn) +(1-αn)Txn strongly converges to a fixed point of T on C.