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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 270954, 16 pages
Hyers-Ulam Stability of Jensen Functional Inequality in p-Banach Spaces
Department of Mathematics, Chungnam National University, 79 Daehangno, Yuseong-gu, Daejeon 305-764, Republic of Korea
Received 2 May 2012; Accepted 6 July 2012
Academic Editor: Nicole Brillouet-Belluot
Copyright © 2012 Hark-Mahn Kim 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.
- S. M. Ulam, A Collection of the Mathematical Problems, Interscience, 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. Aoki, “On the stability of the linear transformation in Banach spaces,” Journal of the Mathematical Society of Japan, vol. 2, pp. 64–66, 1950.
- D. G. Bourgin, “Classes of transformations and bordering transformations,” Bulletin of the American Mathematical Society, vol. 57, pp. 223–237, 1951.
- 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.
- P. Găvruţa, “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.
- S.-M. Jung, “On the Hyers-Ulam-Rassias stability of approximately additive mappings,” Journal of Mathematical Analysis and Applications, vol. 204, no. 1, pp. 221–226, 1996.
- T. M. Rassias, “The stability of mappings and related topics ',” in Report on the 27th ISFE, vol. 39, pp. 292–293, Aequationes mathematicae, 1990.
- Z. Gajda, “On stability of additive mappings,” International Journal of Mathematics and Mathematical Sciences, vol. 14, no. 3, pp. 431–434, 1991.
- T. M. Rassias and P. Šemrl, “On the behavior of mappings which do not satisfy Hyers-Ulam stability,” Proceedings of the American Mathematical Society, vol. 114, no. 4, pp. 989–993, 1992.
- Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis, volume 1, vol. 48 of Colloquium Publications, American Mathematical Society, Providence, RI, USA, 2000.
- S. Rolewicz, Metric Linear Spaces, PWN-Polish Scientific, Warszawa; Reidel, Dordrecht, The Netherlands, 1984.
- M. S. Moslehian and A. Najati, “An application of a fixed point theorem to a functional inequality,” Fixed Point Theory, vol. 10, no. 1, pp. 141–149, 2009.
- H.-M. Kim and E. Son, “Approximate Cauchy functional inequality in quasi-Banach spaces,” Journal of Inequalities and Applications, vol. 2011, article 102, 2011.
- M. S. Moslehian and G. Sadeghi, “Stability of linear mappings in quasi-Banach modules,” Mathematical Inequalities and Applications, vol. 11, no. 3, pp. 549–557, 2008.
- C.-G. Park and T. M. Rassias, “Isometric additive mappings in generalized quasi-Banach spaces,” Banach Journal of Mathematical Analysis, vol. 2, no. 1, pp. 59–69, 2008.
- J. Tabor, “Stability of the Cauchy functional equation in quasi-Banach spaces,” Annales Polonici Mathematici, vol. 83, no. 3, pp. 243–255, 2004.