On Banach contraction principle in a cone metric space

The object of this paper is to establish a generalized form of Banach contraction principle for a cone metric space which is not necessarily normal. This happens to be a generalization of all different forms of Banach contraction Principle, which have been arrived at in L. G. Huang and X. Zhang [L. G. Huang and X. Zhang, J. Math. Anal. Appl 332 (2007), 1468-1476] and Sh. Rezapour, R. Hamlbarani [Sh. Rezapour, R. Hamlbarani, J. Math. Anal. Appl. 345 (2008) 719-724] and D. Ilic, V. Rakocevic [D. Ilic, V. Rakocevic, Applied Mathematics Letters 22 (2009), 728-731]. It also results that the theorem on quasi contraction of Ćirić [L. J. B. Ćirić, Proc. American Mathematical Society 45 (1974), 999-1006]. for a complete metric space also holds good in a complete cone metric space. All the results presented in this paper are new.