Thai Journal of Mathematics Volume x (20xx) Number x : xx–xx http://thaijmath.in.cmu.ac.th ISSN 1686-0209 Common Fixed Point of Generalized Rational Type Contraction Mappings in Partially Ordered Metric Spaces Sumit Chandok † and Erdal Karapinar ‡, 1 † Department of Mathematics, Khalsa College of Engineering & Technology (Punjab Technical University), Ranjit Avenue, Amritsar-143001, India e-mail : chansok.s@gmail.com; chandhok.sumit@gmail.com ‡ Department of Mathematics, Atilim University 06836 Incek, Ankara, Turkey e-mail : ekarapinar@atilim.edu.tr; erdalkarapinar@yahoo.com Abstract : Some common fixed point results for generalized weak contractive condition satisfying rational type expressions in the framework of partially ordered metric spaces are obtained. The proved results generalize and extend some known results in the literature. Keywords : Common fixed point; Weakly compatible mappings; Ordered metric spaces. 2010 Mathematics Subject Classification : 46T99; 47H10; 54H25; 41A50. 1 Introduction and Preliminaries The Banach Contraction Mapping Principle is one of the cornerstone results of nonlinear functional analysis. It is very essential and crucial tool for qualitative nonlinear sciences such as biology, chemistry, physics, various branches of math- ematics etc. In particular, solving existence and uniqueness problems in many different fields of mathematics. Due to its importance and applications poten- tial, The Banach Contraction Mapping Principle has been investigated heavily 1 Corresponding author. Copyright c  2012 by the Mathematical Association of Thailand. All rights reserved.