A New Generalization of Metric Spaces Satisfying the T2-Separation Axiom and Some Related Fixed Point Results.

In this paper, without using neither the compactness nor the uniform convexity, some fixed point theorems are proved by using a binary relation in the setting of a new class of spaces called -partial metric spaces. This class of spaces can be considered the first generalization of metric spaces such that the generated topology is a Hausdorff topology. Our theorems generalize and improve very recent fixed point results in the literature. Finally, we show the existence of a solution for a class of differential equations under new weak conditions. [ABSTRACT FROM AUTHOR]