A general iterative method for nonexpansive mappings in Hilbert spaces

Let H be a real Hilbert space. Consider on H a nonexpansive mapping T with a fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient . Let . It is proved that the sequence {xn} generated by the iterative method xn+1=(I−αnA)Txn+αnγf(xn) converges strongly to a fixed point which solves the variational inequality for x∈Fix(T).