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<p>Abstract</p> <p>In this paper we consider complete cone metric spaces. We generalize some definitions such as <inline-formula> <graphic file="1687-1812-2008-768294-i1.gif"/></inline-formula>-nonexpansive and <inline-formula> <graphic file="1687-1812-2008-768294-i2.gif"/></inline-formula>-uniformly locally contractive functions <inline-formula> <graphic file="1687-1812-2008-768294-i3.gif"/></inline-formula>-closure, <inline-formula> <graphic file="1687-1812-2008-768294-i4.gif"/></inline-formula>-isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.</p>