- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 612576, 4 pages
A Fixed Point Approach to the Stability of an Integral Equation Related to the Wave Equation
Mathematics Section, College of Science and Technology, Hongik University, Sejong 339-701, Republic of Korea
Received 24 July 2013; Accepted 16 October 2013
Academic Editor: Hichem Ben-El-Mechaiekh
Copyright © 2013 Soon-Mo Jung. 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.
- S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York, NY, USA, 1960.
- D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, no. 4, pp. 222–224, 1941.
- T. M. Rassias, “On the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, pp. 297–300, 1978.
- T. Aoki, “On the stability of the linear transformation in Banach spaces,” Journal of the Mathematical Society of Japan, vol. 2, no. 1-2, pp. 64–66, 1950.
- L. Cădariu, “The generalized Hyers-Ulam stability for a class of the Volterra nonlinear integral equations,” Buletinul Stiintific al Universitatii “Politehnica” din Timisoara, vol. 56, no. 70, pp. 30–38, 2011.
- L. Cǎdariu, L. Gǎvruţa, and P. Gǎvruţa, “Weighted space method for the stability of some nonlinear equations,” Applicable Analysis and Discrete Mathematics, vol. 6, no. 1, pp. 126–139, 2012.
- G. L. Forti, “Hyers-Ulam stability of functional equations in several variables,” Aequationes Mathematicae, vol. 50, no. 1-2, pp. 143–190, 1995.
- P. Găvrută, “A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings,” Journal of Mathematical Analysis and Applications, vol. 184, no. 3, pp. 431–436, 1994.
- D. H. Hyers, G. Isac, and M. Th. Rassias, Stability of Functional Equations of Several Variables, Birkhäuser, Basel, Switzerland, 1998.
- D. H. Hyers and T. M. Rassias, “Approximate homomorphisms,” Aequationes Mathematicae, vol. 44, no. 2-3, pp. 125–153, 1992.
- S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, vol. 48 of Springer Optimization and Its Applications, Springer, New York, NY, USA, 2011.
- T. M. Rassias, “On the stability of functional equations and a problem of Ulam,” Acta Applicandae Mathematicae, vol. 62, no. 1, pp. 23–130, 2000.
- L. Cădariu and V. Radu, “On the stability of the Cauchy functional equation: a fixed point approach,” Grazer Mathematische Berichte, vol. 346, pp. 43–52, 2004.
- M. Akkouchi, “Hyers-Ulam-Rassias stability of nonlinear Volterra integral equations via a fixed point approach,” Acta Universitatis Apulensis, vol. 26, pp. 257–266, 2011.
- L. Cădariu and V. Radu, “Fixed points and the stability of Jensen's functional equation,” Journal of Inequalities in Pure and Applied Mathematics, vol. 4, no. 1, Article ID 4, 2003.
- L. P. Castro and A. Ramos, “Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations,” Banach Journal of Mathematical Analysis, vol. 3, no. 1, pp. 36–43, 2009.
- K. Ciepliński, “Applications of fixed point theorems to the Hyers-Ulam stability of functional equations-a survey,” Annals of Functional Analysis, vol. 3, no. 1, pp. 151–164, 2012.
- S.-M. Jung, “A fixed point approach to the stability of isometries,” Journal of Mathematical Analysis and Applications, vol. 329, no. 2, pp. 879–890, 2007.
- V. Radu, “The fixed point alternative and the stability of functional equations,” Fixed Point Theory, vol. 4, no. 1, pp. 91–96, 2003.
- S.-M. Jung, “A fixed point approach to the stability of a volterra integral equation,” Fixed Point Theory and Applications, vol. 2007, Article ID 57064, 9 pages, 2007.
- B. Margolis and J. Diaz, “A fixed point theorem of the alternative for contractions on a generalized complete metric space,” Bulletin of the American Mathematical Society, vol. 74, pp. 305–309, 1968.