We prove the existence of common fixed points of a
generalized contraction / Zamfirescu pair of maps in a complete cone metric
space. Our results generalize the results of Haung anf Zhang [L-G. Haung, X. Zhang: Cone metric spaces and fixed
point theorems of contractive mappings, J. Math. Anal. Appl.
332 (2007) 1468--1476]
and extend the results of Rezapour and Hamlbarani [Sh. Rezapour, R. Hamlbarani: Some notes on the
paper ``Cone metric spaces and fixed point theorems of contractive
mappings", J. Math. Anal. Appl. 345 (2008) 719--724].