Let X be a uniformly smooth real Banach space. Let T:X → X be continuos and strongly accretive operator. For a given f e X, define S: X → X by Sx =f−Tx+x, for all x e X. Let {an} n=0 ∞ , {βn} n=0 ∞ be two real sequences in (0, 1) satisfying: $$a_n \to 0,\beta _n \to 0, as n \to \infty$$ (i) ; $$\sum\limits_{n = 0}^\infty {\alpha _n = \infty }$$ (ii) Assume that {un} n=0 ∞ and {υn} n=0 ∞ are two sequences in X satisfying ‖un‖ = 0(αn) and ‖υn‖ → 0 as n → ∞. For arbitrary x0 e X, the iteration sequence {xn} is defined by $$(IS)\left\{ \begin{gathered} x_{n + 1} = (1 - \alpha _n )x_n + \alpha _n Sy_n + u_n ; \hfill \\ y_n = (1 - \beta _n )x_n + \beta _n Sx_n + \upsilon _n (n \geqslant 0) \hfill \\ \end{gathered} \right.$$ (1) Moreover, suppose that {Sxn} and {Syn} are bounded, then {xn} converges strongly to the unique fixed point of S.