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Journal of Function Spaces
Volume 2016, Article ID 6978439, 9 pages
http://dx.doi.org/10.1155/2016/6978439
Research Article

A New Approach to the Study of Fixed Point Theorems with -Distances via -Functions

1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Young Researcher and Elite Club, Arak-Branch, Islamic Azad University, Arak, Iran
3Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran

Received 5 June 2016; Revised 28 July 2016; Accepted 24 August 2016

Academic Editor: Francesca Vetro

Copyright © 2016 Farzad Zarinfar 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 introduce some new generalization of fixed point theorems in complete metric spaces endowed with -distances via -functions. Our results extend many of known fixed point theorems such as Reich type contraction, Geraghty contraction, Meir-Keeler contraction, and -contraction. In addition, the result and corollaries show that our approach has a constructive attitude and many known and unknown results can be constructed in such way.