In this paper we consider complete cone metric spaces. We generalize some definitions such as [inline-graphic not available: see fulltext]-nonexpansive and [inline-graphic not available: see fulltext]-uniformly locally contractive functions [inline-graphic not available: see fulltext]-closure, [inline-graphic not available: see fulltext]-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.