Properties of C-metric spaces

• Published in: AIP conference proceedings Vol. 1872; no. 1
• Main Authors: Croitoru, Anca, Apreutesei, Gabriela, Mastorakis, Nikos E.
• Format: Journal Article
• Language: English
• Published: 06.09.2017
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/1.4996673

The subject of this paper belongs to the theory of approximate metrics [23]. An approximate metric on X is a real application defined on X × X that satisfies only a part of the metric axioms. In a recent paper [23], we introduced a new type of approximate metric, named C-metric, that is an application which satisfies only two metric axioms: symmetry and triangular inequality. The remarkable fact in a C-metric space is that a topological structure induced by the C-metric can be defined. The innovative idea of this paper is that we obtain some convergence properties of a C-metric space in the absence of a metric. In this paper we investigate C-metric spaces. The paper is divided into four sections. Section 1 is for Introduction. In Section 2 we recall some concepts and preliminary results. In Section 3 we present some properties of C-metric spaces, such as convergence properties, a canonical decomposition and a C-fixed point theorem. Finally, in Section 4 some conclusions are highlighted.