Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2012, Article ID 382094, 12 pages doi:10.1155/2012/382094 Research Article Common Fixed Point Results Using Generalized Altering Distances on Orbitally Complete Ordered Metric Spaces Hemant Kumar Nashine, 1 Zoran Kadelburg, 2 and Zorana Golubovi´ c 3 1 Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Raipur 492101, India 2 Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia 3 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia Correspondence should be addressed to Zoran Kadelburg, kadelbur@matf.bg.ac.rs Received 9 December 2011; Accepted 21 March 2012 Academic Editor: Giuseppe Marino Copyright q 2012 Hemant Kumar Nashine et al. 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. We prove the existence of common fixed points for three relatively asymptotically regular map- pings defined on an orbitally complete ordered metric space using orbital continuity of one of the involved maps. We furnish a suitable example to demonstrate the validity of the hypotheses of our results. 1. Introduction and Preliminaries Browder and Petryshyn introduced the concept of asymptotic regularity of a self-map at a point in a metric space. Definition 1.1 see 1. A self-map T on a metric space X,d is said to be asymptotically regular at a point x ∈X if lim n →∞ dT n x, T n1 x 0. Recall that the set Ox 0 ; T {T n x 0 : n  0, 1, 2,...} is called the orbit of the self-map T at the point x 0 ∈X. Definition 1.2 see 2. A metric space X,d is said to be T-orbitally complete if every Cauchy sequence contained in Ox; Tfor some x in X converges in X.