Metric-like spaces, partial metric spaces and fixed points

Abstract

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 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. © 2012 Amini-Harandi; licensee Springer.