Journal of Applied Mathematics
Volume 2012 (2012), Article ID 856974, 7 pages
http://dx.doi.org/10.1155/2012/856974
Research Article

Periodic Points and Fixed Points for the Weaker ( 𝜙 , 𝜑 ) -Contractive Mappings in Complete Generalized Metric Spaces

Chi-Ming Chen and W. Y. Sun

Department of Applied Mathematics, National Hsinchu University of Education, No. 521 Nanda Road, Hsinchu City 300, Taiwan

Received 19 November 2011; Accepted 14 December 2011

Academic Editor: Song Cen

Copyright © 2012 Chi-Ming Chen and W. Y. Sun. 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 the notion of weaker ( 𝜙 , 𝜑 ) -contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.