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Abstract and Applied Analysis
Volume 2014, Article ID 171624, 8 pages
Research Article

Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces

1Department of Mathematics, Texas A&M University-Kingsville, MSC 172, Rhode Hall 217B, Kingsville, TX 78363-8202, USA
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia
4Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey
5Department of Mathematics, Islamic Azad University, Arak Branch, Arak, Iran

Received 17 March 2014; Accepted 18 April 2014; Published 21 May 2014

Academic Editor: Wei-Shih Du

Copyright © 2014 Ravi P. Agarwal et al. 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.


Very recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces.