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Let X be a uniformly smooth real Banach space. Let T:X → X be continuos and strongly accretive operator. For a given f ε X, define S: X → X by Sx =f−Tx+x, for all x ε X. Let {an}, {βn}be two real sequences in (0, 1) satisfying:; Assume that {un} and {υn} are two sequences in X satisfying |un| = 0(αn) and |υn| → 0 as n → ∞. For arbitrary x0 ε X, the iteration sequence {xn} is defined by Moreover, suppose that {Sxn} and {Syn} are bounded, then {xn} converges strongly to the unique fixed point of S. [ABSTRACT FROM AUTHOR]