Abstract and Applied Analysis
Volume 2012 (2012), Article ID 386253, 15 pages
http://dx.doi.org/10.1155/2012/386253
Research Article

Implicit-Relation-Type Cyclic Contractive Mappings and Applications to Integral Equations

Hemant Kumar Nashine,1 Zoran Kadelburg,2 and Poom Kumam3

1Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Chhattisgarh, Raipur 492101, India
2Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Beograd, Serbia
3Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand

Received 28 July 2012; Accepted 5 September 2012

Academic Editor: Sehie Park

Copyright © 2012 Hemant Kumar Nashine 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 an implicit-relation-type cyclic contractive condition for a map in a metric space and derive existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the paper, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented.