We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

This paper is concerned with mixed monotone mappings in partially ordered cone metric spaces. We establish several fixed point theorems, which generalize and complement some known results. Especially, even in a partially ordered metric space, our main results are generalizations of the fixed point theorems due to Bhaskar and Lakshmikantham [T. Grana Bhaskar, V. Lakshmikantham, Fixed point theor...

Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.

For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat(0) space and Gromov hyperbolic. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.

*Correspondence: [email protected] Faculty of Mathematics and Informatics, University of Plovdiv, Plovdiv, 4000, Bulgaria Abstract In this paper, we establish a full statement of Ćirić’s fixed point theorem in the setting of cone metric spaces. More exactly, we obtain a priori and a posteriori error estimates for approximating fixed points of quasi-contractions in a cone metric space. Our ...

For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat(0) space. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.

For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat(0) space. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.