On Banach contraction principle in a cone metric space
- Quantum School of Technology, Roorkee (U. K.), India.
- Shri Vaishnav Institute of Technology and Science, Indore (M. P.), India.
Lal Bahadur Jain
- Retd. Principal, Govt. Arts and Commerce College ), Indore (M. P.), India.
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.
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Shobha Jain, Shishir Jain, Lal Bahadur Jain, On Banach contraction principle in a cone metric space, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 4, 252--258
Jain Shobha, Jain Shishir, Jain Lal Bahadur, On Banach contraction principle in a cone metric space. J. Nonlinear Sci. Appl. (2012); 5(4):252--258
Jain, Shobha, Jain, Shishir, Jain, Lal Bahadur. "On Banach contraction principle in a cone metric space." Journal of Nonlinear Sciences and Applications, 5, no. 4 (2012): 252--258
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