In this paper we extend fixed point theorems of Ciric ([Lj. Ciric, On a family of contractive maps and fixed points, Publ. Inst. Math., 17(31), (1974), 45-51; Some Recent Results in Metrical Fixed Point Theory, Beograd 2003.]) from the metric space to cone metric spaces.
We do not impose the normality property on the cone, but suppose only that the cone P in the real ordered Banach space E has a nonempty interior. Thus our results generalize and extend fixed point theorems of contractive mappings in several aspect ( see: Remark 3.3 and Corollaries 3.4-3.8). Three examples are given to illustrate the usability of our results.