Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 5 (2012), 252–258 Research Article On Banach contraction principle in a cone metric space Shobha Jain a , Shishir Jain b,∗ , Lal Bahadur Jain c a Quantum School of Technology, Roorkee (U.K), India. b Shri Vaishnav Institute of Technology and Science, Indore (M.P.), India. c Retd. Principal,Govt. Arts and Commerce College Indore (M.P.), India. This paper is dedicated to Professor Ljubomir ´ Ciri´ c Communicated by Professor V. Berinde Abstract 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 ˜ Ciri˜ c [L. J. B. ˜ Ciri˜ c, 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. c 2012. All rights reserved. Keywords: Cone metric space, common fixed points. 1. Introduction There has been a number of generalizations of metric space. One such generalization is a cone metric space. In the second half of previous century a lot of work has been done in a K-metric space, which is in the setting of cone in a real normed linear space and variously defined notions of convergence and a Cauchy * Corresponding author Email addresses: shobajain1@yahoo.com ( Shobha Jain), jainshishir11@rediffmail.com (Shishir Jain), lalbahdurjain11@yahoo.com ( Lal Bahadur Jain) Received 2011-4-14