Applied Mathematical Sciences, Vol. 8, 2014, no. 66, 3263 - 3272 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.44319 Common Fixed Point Theorems for Compatible Mappings of Type(C) in BA-Cone Metric Spaces Neslihan Kaplan Department of Mathematics, Sakarya University, 54187, Sakarya, Turkey Mahpeyker ¨ Ozt¨ urk Department of Mathematics, Sakarya University, 54187, Sakarya, Turkey Copyright c  2014 Neslihan Kaplan and Mahpeyker ¨ Ozt¨ urk. This is an open access article distributed under the Creative Commons Attribution License, which permits unre- stricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The purpose of this paper is to establish common fixed point theo- rems for four self-mappings using the concepts of compatible mappings of type(C) and weakly compatibility of pairs through rational expres- sions in a BA-cone metric space. Mathematics Subject Classification: 47H10, 54H25 Keywords: Cone metric space, Rational expressions, Compatible map- pings of type(C), Weakly compatibility, Banach algebra 1 Introduction The Banach contraction principle is one of the cornerstone results of nonlinear functional analysis. Due to its usefulness and applications, it has become a very crucial and popular tool in solving existence and uniqueness problems in many different fields of mathematics. This principle has been extended to other kinds of contraction principle, such as contractive conditions involving