In this paper, we will prove the following: Let D be a nonempty of a normed linear space X and T : D -> X be a nonexpansive mapping. Let ${x_n}$ be a sequence in D and ${t_n}$, ${s_n}$ be real sequences such that (i) $0;{leq};t_n;{leq};t;<;1;and;{sum_{n=1}}^{infty};t_n;=;{infty},;(ii);(a);0;{leq};s_n;{leq};1,;s_n;->;0;as;n;->;{infty};and;{sum_{n=1}}^{infty};t_ns_n;<;{infty};or;(b);s_n;=;s;for;all;n;{geq};1;and;s;{in};[0,1),;(iii);x_{n+1};=;(1-t_n)x_n+t_nT(s_nTx_n+(1-s_n)x_n);for;all;n;{geq};1.$ Then, if the sequence {x_n} is bounded, then $lim_{n->infty};$mid$$mid$x_n-Tx_n$mid$$mid$;=;0$</TEX>. This result improves and complements a result of Deng [2]. Furthermore, we will show that certain conditions on D, X and T guarantee the weak and strong convergence of the Ishikawa iterative sequence to a fixed point of T.