Metric-like spaces, partial metric spaces and fixed points

By a metric-like space, as a generalization of a partial metric space, we mean a pair ( X , σ ) , where X is a nonempty set and σ : X × X → R satisfies all of the conditions of a metric except that σ ( x , x ) may be positive for x ∈ X . In this paper, we initiate the fixed point theory in metric-like spaces. As an application, we derive some new fixed point results in partial metric spaces. Our results unify and generalize some well-known results in the literature. MSC: 47H10.