International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 431872, 11 pages
http://dx.doi.org/10.1155/2012/431872
Research Article

An Extension of Generalized ( 𝜓 , 𝜑 ) -Weak Contractions

Tran Van An,1 Kieu Phuong Chi,1 Erdal Karapınar,2 and Tran Duc Thanh1

1Department of Mathematics, Vinh University, 182 Le Duan, Vinh City, Vietnam
2Department of Mathematics, Atilim University, İncek, 06836 Ankara, Turkey

Received 6 February 2012; Accepted 23 May 2012

Academic Editor: A. Zayed

Copyright © 2012 Tran Van An 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 prove a fixed-point theorem for a class of maps that satisfy generalized ( 𝜓 , 𝜑 ) -weak contractions depending on a given function. An example is given to illustrate our extensions.