Gen. Math. Notes, Vol. 21, No. 1, March 2014, pp.10-26 ISSN 2219-7184; Copyright c ICSRS Publication, 2014 www.i-csrs.org Available free online at http://www.geman.in Generalized c-Distance and a Common Fixed Point Theorem in Cone Metric Spaces Sushanta Kumar Mohanta 1 and Rima Maitra 2 1,2 Department of Mathematics, West Bengal State University Barasat, 24 Parganas (North), West Bengal Kolkata 700126, India 1 E-mail: smwbes@yahoo.in 2 E-mail: rima.maitra.barik@gmail.com (Received: 3-1-14 / Accepted: 12-2-14) Abstract The main purpose of this work is to obtain a common fixed point theorem for a pair of self mappings in cone metric spaces by using the concept of generalized c-distance. Our results will improve and supplement some results in the existing literature. Finally, an example is provided to show that the generalized c- distances form a bigger category than that of c-distances. Keywords: c-Distance, Generalized c-distance, Point of coincidence, Weakly compatible mappings, Common fixed point. 1 Introduction Over the past two decades a considerable amount of research work for the de- velopment of fixed point theory have executed by several authors. There has been a number of generalizations of the usual notion of a metric space. One such generalization is a cone metric space initiated by Huang and Zhang[8]. After that a series of articles have been dedicated to the improvement of fixed point theory. In most of those articles, the authors used normality property of cones in their results. The idea of common fixed point was initially given by Junck[11]. In fact, they considered commuting mappings to obtain common