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Abstract and Applied Analysis
Volume 2014, Article ID 258985, 9 pages
Research Article

Fixed Point Theorems in Quaternion-Valued Metric Spaces

1Mathematics Department, Faculty of Science, Taif University, Taif 888, Saudi Arabia
2Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
3Mathematics Department, Faculty of Science, South Valley University, Qena, Egypt

Received 8 October 2013; Revised 14 January 2014; Accepted 23 January 2014; Published 30 March 2014

Academic Editor: Naseer Shahzad

Copyright © 2014 Ahmed El-Sayed Ahmed 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.


The aim of this paper is twofold. First, we introduce the concept of quaternion metric spaces which generalizes both real and complex metric spaces. Further, we establish some fixed point theorems in quaternion setting. Secondly, we prove a fixed point theorem in normal cone metric spaces for four self-maps satisfying a general contraction condition.