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v Research Article A Generalisation of Contraction Principle in Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 406368 8 pages doi 10.1155 2008 406368 Research Article A Generalisation of Contraction Principle in Metric Spaces P. N. Dutta1 and Binayak S. Choudhury2 1 Department of Mathematics Government College of Engineering and Ceramic Technology 73 A.C. Banerjee Lane Kolkata West Bengal 700010 India 2 Department of Mathematics Bengal Engineering and Science University P.O. Botanical Garden Shibpur Howrah West Bengal 711103 India Correspondence should be addressed to P. N. Dutta prasanta_dutta1@yahoo.co.in Received 28 March 2008 Revised 26 June 2008 Accepted 18 August 2008 Recommended by Gorniewicz Lech Here we introduce a generalisation of the Banach contraction mapping principle. We show that the result extends two existing generalisations of the same principle. We support our result by an example. Copyright 2008 P. N. Dutta and B. S. Choudhury. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Banach contraction mapping principle is one of the pivotal results of analysis. It is widely considered as the source of metric fixed point theory. Also its significance lies in its vast applicability in a number of branches of mathematics. T X X where X d is a complete metric space is said to be a contraction mapping if for all x y e X d Tx Ty kd x y where 0 k 1. 1.1 According to the contraction mapping principle any mapping T satisfying 1.1 will have a unique fixed point. Generalisation of the above principle has been a heavily investigated branch of research. The following are a few examples of such generalisations. In 1 Boyd and Wong proved that the constant k in 1.1 can be replaced by the use of an upper semicontinuous function. In 2 3 generalised Banach contraction conjecture has been established. In 4 Suzuki has