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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 293101, 8 pages
http://dx.doi.org/10.1155/2013/293101
Research Article

Fixed-Point Theorems in Complete Gauge Spaces and Applications to Second-Order Nonlinear Initial-Value Problems

1Department of Mathematics, Faculty of Sciences of Tunis, University Campus, 2092 Tunis, Tunisia
2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
3Università degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi 34, 90123 Palermo, Italy

Received 3 May 2013; Accepted 10 August 2013

Academic Editor: Anna Kamińska

Copyright © 2013 Meryam Cherichi 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 establish fixed-point results for mappings and cyclic mappings satisfying a generalized contractive condition in a complete gauge space. Our theorems generalize and extend some fixed-point results in the literature. We apply our obtained results to the study of existence and uniqueness of solution to a second-order nonlinear initial-value problem.