Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 508730, 10 pages doi:10.1155/2011/508730 Research Article Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces Ishak Altun and Ali Erduran Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey Correspondence should be addressed to Ishak Altun, ishakaltun@yahoo.com Received 12 November 2010; Accepted 24 December 2010 Academic Editor: S. Al-Homidan Copyright q 2011 I. Altun and A. Erduran. 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. Matthews 1994 introduced a new distance p on a nonempty set X, which is called partial metric. If X, p is a partial metric space, then px, x may not be zero for x ∈ X. In the present paper, we give some fixed point results on these interesting spaces. 1. Introduction There are a lot of fixed and common fixed point results in different types of spaces. For example, metric spaces, fuzzy metric spaces, and uniform spaces. One of the most interesting is partial metric space, which is defined by Matthews 1. In partial metric spaces, the distance of a point in the self may not be zero. After the definition of partial metric space, Matthews proved the partial metric version of Banach fixed point theorem. Then, Valero 2, Oltra and Valero 3, and Altun et al. 4 gave some generalizations of the result of Matthews. Again, Romaguera 5 proved the Caristi type fixed point theorem on this space. First, we recall some definitions of partial metric spaces and some properties of theirs. See 1–3, 5–7 for details. A partial metric on a nonempty set X is a function p : X × X →  such that for all x, y, z ∈ X : p 1  x  y ⇔ px, x px, y py, y, p 2  px, x ≤ px, y,