On Banach contraction principle in a cone metric space

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Authors
Shobha Jain
 Quantum School of Technology, Roorkee (U. K.), India.
Shishir Jain
 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.
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), 14681476] and Sh. Rezapour, R. Hamlbarani [Sh. Rezapour, R.
Hamlbarani, J. Math. Anal. Appl. 345 (2008) 719724] and D. Ilic, V. Rakocevic [D. Ilic, V. Rakocevic,
Applied Mathematics Letters 22 (2009), 728731]. It also results that the theorem on quasi contraction of
Ćirić [L. J. B. Ćirić, Proc. American Mathematical Society 45 (1974), 9991006]. for a complete metric
space also holds good in a complete cone metric space. All the results presented in this paper are new.
Share and Cite
ISRP Style
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, 252258
AMA Style
Jain Shobha, Jain Shishir, Jain Lal Bahadur, On Banach contraction principle in a cone metric space. J. Nonlinear Sci. Appl. (2012); 5(4):252258
Chicago/Turabian Style
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): 252258
Keywords
 Cone metric space
 common fixed points.
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