- 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 269701, 10 pages
Probabilistic (Quasi)metric Versions for a Stability Result of Baker
Department of Mathematics, West University of Timişoara, 4 V. Pârvan Boulevard, 300223 Timişoara, Romania
Received 8 June 2012; Revised 15 October 2012; Accepted 18 October 2012
Academic Editor: Bing Xu
Copyright © 2012 Dorel Miheţ and Claudia Zaharia. 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.
- J. A. Baker, “The stability of certain functional equations,” Proceedings of the American Mathematical Society, vol. 112, no. 3, pp. 729–732, 1991.
- V. Radu, “The fixed point alternative and the stability of functional equations,” Fixed Point Theory, vol. 4, no. 1, pp. 91–96, 2003.
- 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, 7 pages, 2003.
- D. Miheţ and V. Radu, “On the stability of the additive Cauchy functional equation in random normed spaces,” Journal of Mathematical Analysis and Applications, vol. 343, no. 1, pp. 567–572, 2008.
- D. Miheţ, “The fixed point method for fuzzy stability of the Jensen functional equation,” Fuzzy Sets and Systems, vol. 160, no. 11, pp. 1663–1667, 2009.
- A. K. Mirmostafaee, “A fixed point approach to almost quartic mappings in quasi fuzzy normed spaces,” Fuzzy Sets and Systems, vol. 160, no. 11, pp. 1653–1662, 2009.
- D. Miheţ, “The probabilistic stability for a functional nonlinear equation in a single variable,” Journal of Mathematical Inequalities, vol. 3, no. 3, pp. 475–483, 2009.
- M. E. Gordji and H. Khodaei, “The fixed point method for fuzzy approximation of a functional equation associated with inner product spaces,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 140767, 15 pages, 2010.
- H. A. Kenary and Y. J. Cho, “Stability of mixed additive-quadratic Jensen type functional equation in various spaces,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2704–2724, 2011.
- C. Park, J. R. Lee, and D. Y. Shin, “Generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation,” Applied Mathematics Letters, vol. 25, no. 2, pp. 200–205, 2012.
- A. Ebadian, M. Eshaghi Gordji, H. Khodaei, R. Saadati, and Gh. Sadeghi, “On the stability of an m-variables functional equation in random normed spaces via fixed point method,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 346561, 13 pages, 2012.
- B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing, New York, 1983.
- O. Hadžić, “On the -topology of probabilistic locally convex spaces,” Glasnik Matematički III, vol. 13, no. 33, pp. 293–297, 1978.
- O. Hadžić and M. Budincevic, “A fixed point theorem in PM spaces,” Colloquia Mathematica Societatis Janos Bolyai, vol. 23, pp. 569–579, 1978.
- V. Radu, “On the t-norms of the Hadžić type and fixed points in probabilistic metric spaces,” Review of Research, vol. 13, pp. 81–85, 1983.
- V. M. Sehgal and A. T. Bharucha-Reid, “Fixed points of contraction mappings on probabilistic metric spaces,” Mathematical Systems Theory, vol. 6, pp. 97–102, 1972.
- O. Hadžić and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001.
- D. Miheţ, “The probabilistic stability for a functional equation in a single variable,” Acta Mathematica Hungarica, vol. 123, no. 3, pp. 249–256, 2009.
- Y. J. Cho, M. Grabiec, and V. Radu, On Nonsymmetric Topological and Probabilistic Structures, Nova Science Publishers, New York, NY, USA, 2006.
- D. Miheţ, “A note on a fixed point theorem in Menger probabilistic quasi-metric spaces,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2349–2352, 2009.