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Journal of Function Spaces
Volume 2016, Article ID 6759320, 5 pages
http://dx.doi.org/10.1155/2016/6759320
Research Article

A New Approach for the Approximations of Solutions to a Common Fixed Point Problem in Metric Fixed Point Theory

1College of Science, King Saud University, Riyadh, Saudi Arabia
2Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey
3College of Science, Geology and Geophysics Department, King Saud University, Riyadh 11451, Saudi Arabia
4Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
5College of Engineering, Petroleum and Natural Gas Engineering Department, King Saud University, Riyadh 11421, Saudi Arabia
6Faculty of Science, Geology Department, Benha University, Benha 13518, Egypt

Received 3 July 2016; Accepted 18 September 2016

Academic Editor: Filomena Cianciaruso

Copyright © 2016 Ishak Altun 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.

Abstract

We provide sufficient conditions for the existence of a unique common fixed point for a pair of mappings , where is a nonempty set endowed with a certain metric. Moreover, a numerical algorithm is presented in order to approximate such solution. Our approach is different to the usual used methods in the literature.