For an asymptotically non-expansive self-mapping T, we will prove the strong convergence of {xn} defined by xn+1 = (1−an−bn)xn+anu+bnTnxn, xn+1 = anu+(1−an)Tnxn, whenever {bn}, {an}Ì (0,1) satisfy (C1) limn®¥ an=0, (C2) S¥n=0 =¥ (C3) limn®¥ Kn-1/an = 0 or (C4) S¥n=0 (kn-1)<+¥ application, we also establish the strong convergence of the viscosity approximation schemes with a contraction ¦ given by
xn+1 = anf (xn) + (1 −an)Tnxn
and
xn+1 = (1 −an− bn)xn+an f(xn) +bnTnxn.