TY - JOUR AU - Jain, Shobha AU - Jain, Shishir AU - Jain, Lal Bahadur PY - 2012 TI - On Banach contraction principle in a cone metric space JO - Journal of Nonlinear Sciences and Applications SP - 252--258 VL - 5 IS - 4 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.005.04.01 DO - 10.22436/jnsa.005.04.01 ID - Jain2012 ER - TY - BOOK TI - Itrative approximation of fixed points AU - V. Berinde PB - Springer Verlag PY - 2007 DA - 2007// CY - ID - Berinde2007 ER - TY - JOUR TI - A generalization of Banach contraction princple AU - L. J. B. Ćirić JO - Proc. American Mathematical Society PY - 1974 DA - 1974// VL - 45 ID - Ćirić1974 ER - TY - JOUR TI - Cone metric spaces and fixed point theorems of contractive mappings AU - L. G. Huang AU - X. Zhang JO - J. Math. Anal. Appl. PY - 2007 DA - 2007// VL - 332 ID - Huang2007 ER - TY - JOUR TI - Quasi-contraction on a cone metric space AU - D. Ilic AU - V. Rakocevic JO - Applied Mathematics Letters PY - 2009 DA - 2009// VL - 22 ID - Ilic2009 ER - TY - JOUR TI - Compatibilty and weak compatibility for four self maps in a cone metric space AU - Sh. Jain AU - Sh. Jain AU - L. B. Jain JO - Bulletin of Mathematical analysis and application PY - 2010 DA - 2010// VL - 1 ID - Jain2010 ER - TY - JOUR TI - Weakly compatibile maps in a cone metric space AU - Sh. Jain AU - Sh. Jain AU - L. B. Jain JO - Rendiconti Del Seminario Matematica PY - 2010 DA - 2010// VL - 68 ID - Jain2010 ER - TY - JOUR TI - On some boundary value problems AU - B. V. Kvedaras AU - A. V. Kibenko AU - A. I. Perov JO - Litov. matem. sbornik PY - 1965 DA - 1965// VL - 5 ID - Kvedaras1965 ER - TY - JOUR TI - Fixed point principle in generalized metric space AU - E. M. Mukhamadiev AU - V. J. Stetsenko JO - Izvestija AN Tadzh. SSR, fiz.-mat. i geol.-chem. nauki. PY - 1969 DA - 1969// VL - 10 ID - Mukhamadiev1969 ER - TY - JOUR TI - The Cauchy problem for systems of ordinary differential equations AU - A. I. Perov JO - In , Approximate methods of solving differential equations, Kiev, Naukova Dumka PY - 12 DA - 12// VL - 1964 ID - Perov 12 ER - TY - JOUR TI - An approach to studying boundary value problems AU - A. I. Perov AU - A. V. Kibenko JO - Izvestija AN SSSR, ser. math. PY - 1966 DA - 1966// VL - 30 ID - Perov1966 ER - TY - JOUR TI - Some notes on the paper ''Cone metric spaces and fixed point theorems of contractive mappings'' AU - h. Rezapour AU - R. Hamlbarani JO - J. Math. Anal. Appl. PY - 2008 DA - 2008// VL - 345 ID - Rezapour2008 ER - TY - JOUR TI - A Fixed Point Theorem for a sequence of Maps satisfying a new contractive type contraction in Menger Space AU - R. Vasuki JO - Math Japonica PY - 1990 DA - 1990// VL - 35 ID - Vasuki 1990 ER - TY - JOUR TI - K-metric and K-normed linear spaces AU - P. P. Zabrejko JO - Survey Collect. Math. PY - 1997 DA - 1997// VL - 48 ID - Zabrejko1997 ER -