Fixed and periodic point results in cone metric spaces

Huang and Zhang [L.-G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476] proved some fixed point theorems in cone metric spaces. In this work we prove some fixed point theorems in cone metric spaces, including results which generalize those from Haung and Zhang’s work. Given the fact that, in a cone, one has only a partial ordering, it is doubtful that their Theorem 2.1 can be further generalized. We also show that these maps have no nontrivial periodic points.