- About this Journal ·
- Abstracting and Indexing ·
- 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 2012 (2012), Article ID 205160, 10 pages
A Fixed Point Approach to the Stability of a Cauchy-Jensen Functional Equation
1Graduate School of Education, Kyung Hee University, Yongin 446-701, Republic of Korea
2Department of Mathematics Education, College of Education, Mokwon University, Daejeon 302-729, Republic of Korea
Received 16 February 2012; Revised 6 April 2012; Accepted 20 April 2012
Academic Editor: Krzysztof Cieplinski
Copyright © 2012 Jae-Hyeong Bae and Won-Gil Park. 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, Problems in Modern Mathematics, Wiley, 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, 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, no. 2, pp. 297–300, 1978.
- 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, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, vol. 48 of Springer Optimization and Its Applications, Springer, New York, NY, USA, 2011.
- M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Birkhäuser, Basle, Switzerland, 2nd edition, 2009.
- P. K. Sahoo and P. Kannappan, Introduction to Functional Equations, CRC Press, Boca Raton, Fla, USA, 2011.
- W.-G. Park and J.-H. Bae, “On a Cauchy-Jensen functional equation and its stability,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 634–643, 2006.
- B. Margolis and J. B. 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.
- 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 4, 2003.
- J.-H. Bae and W.-G. Park, “Stability of a Cauchy-Jensen functional equation in quasi-Banach spaces,” Journal of Inequalities and Applications, vol. 2010, Article ID 151547, 9 pages, 2010.