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<p/> <p>In real Hilbert space <inline-formula><graphic file="1687-1812-2007-028619-i1.gif"/></inline-formula>, from an arbitrary initial point <inline-formula><graphic file="1687-1812-2007-028619-i2.gif"/></inline-formula>, an explicit iteration scheme is defined as follows: <inline-formula><graphic file="1687-1812-2007-028619-i3.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1812-2007-028619-i4.gif"/></inline-formula>, <inline-formula><graphic file="1687-1812-2007-028619-i5.gif"/></inline-formula> is a nonexpansive mapping such that <inline-formula><graphic file="1687-1812-2007-028619-i6.gif"/></inline-formula> is nonempty, <inline-formula><graphic file="1687-1812-2007-028619-i7.gif"/></inline-formula> is a <inline-formula><graphic file="1687-1812-2007-028619-i8.gif"/></inline-formula>-strongly monotone and <inline-formula><graphic file="1687-1812-2007-028619-i9.gif"/></inline-formula>-Lipschitzian mapping, <inline-formula><graphic file="1687-1812-2007-028619-i10.gif"/></inline-formula>, and <inline-formula><graphic file="1687-1812-2007-028619-i11.gif"/></inline-formula>. Under some suitable conditions, the sequence <inline-formula><graphic file="1687-1812-2007-028619-i12.gif"/></inline-formula> is shown to converge strongly to a fixed point of <inline-formula><graphic file="1687-1812-2007-028619-i13.gif"/></inline-formula> and the necessary and sufficient conditions that <inline-formula><graphic file="1687-1812-2007-028619-i14.gif"/></inline-formula> converges strongly to a fixed point of <inline-formula><graphic file="1687-1812-2007-028619-i15.gif"/></inline-formula> are obtained.</p>