Geodesic
On Banach contraction principle in a cone metric space
Jain, Shobha1 ; Jain, Shishir2 ; Jain, Lal Bahadur3
1 Quantum School of Technology, Roorkee (U. K.), India
2 Shri Vaishnav Institute of Technology and Science, Indore (M. P.), India
3 Retd. Principal, Govt. Arts and Commerce College ), Indore (M. P.), India
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 4, p. 252-258.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.005.04.01
Keywords: Cone metric space, common fixed points.

Jain, Shobha 1 ; Jain, Shishir 2 ; Jain, Lal Bahadur 3

1 Quantum School of Technology, Roorkee (U. K.), India
2 Shri Vaishnav Institute of Technology and Science, Indore (M. P.), India
3 Retd. Principal, Govt. Arts and Commerce College ), Indore (M. P.), India 
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Jain, Shobha; Jain, Shishir; Jain, Lal Bahadur. On Banach contraction principle in a cone metric space. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 4, p. 252-258. doi : 10.22436/jnsa.005.04.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.04.01/

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