Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces

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 :