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Journal of Mathematics
Volume 2016, Article ID 4746732, 6 pages
Research Article

On Parametric -Metric Spaces and Fixed-Point Type Theorems for Expansive Mappings

Department of Mathematics, Balıkesir University, 10145 Balıkesir, Turkey

Received 29 July 2016; Revised 11 October 2016; Accepted 16 October 2016

Academic Editor: Kaleem R. Kazmi

Copyright © 2016 Nihal Taş and Nihal Yılmaz Özgür. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce the notion of a parametric -metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametric -metric space. It is important to obtain new fixed-point theorems on a parametric -metric space because there exist some parametric -metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametric -metric space.