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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 435310, 15 pages
On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions
Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of Korea
Received 29 August 2012; Accepted 18 October 2012
Academic Editor: Abdelghani Bellouquid
Copyright © 2012 Jae-Young Chung. 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 Tracts in Pure and Applied Mathematics, no. 8, 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, pp. 222–224, 1941.
- G. L. Forti, “The stability of homomorphisms and amenability, with applications to functional equations,” Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 57, pp. 215–226, 1987.
- Z. Daróczy, “On a functional equation of Hosszù type,” Mathematica Pannonica, vol. 10, no. 1, pp. 77–82, 1999.
- K. J. Heuvers, “Another logarithmic functional equation,” Aequationes Mathematicae, vol. 58, no. 3, pp. 260–264, 1999.
- K. J. Heuvers and P. Kannappan, “A third logarithmic functional equation and Pexider generalizations,” Aequationes Mathematicae, vol. 70, no. 1-2, pp. 117–121, 2005.
- L. Schwartz, Théorie des Distributions, Hermann, Paris, France, 1966.
- J. A. Baker, “Distributional methods for functional equations,” Aequationes Mathematicae, vol. 62, no. 1-2, pp. 136–142, 2001.
- E. Y. Deeba and E. L. Koh, “The Pexider functional equations in distributions,” Canadian Journal of Mathematics, vol. 42, no. 2, pp. 304–314, 1990.
- E. Deeba and S. Xie, “Distributional analog of a functional equation,” Applied Mathematics Letters, vol. 16, no. 5, pp. 669–673, 2003.
- E. Deeba, P. K. Sahoo, and S. Xie, “On a class of functional equations in distribution,” Journal of Mathematical Analysis and Applications, vol. 223, no. 1, pp. 334–346, 1998.
- J. Chung, S.-Y. Chung, and D. Kim, “The stability of Cauchy equations in the space of Schwartz distributions,” Journal of Mathematical Analysis and Applications, vol. 295, no. 1, pp. 107–114, 2004.
- J. Chung, “Hyers-Ulam stability theorems for Pexider equations in the space of Schwartz distributions,” Archiv der Mathematik, vol. 84, no. 6, pp. 527–537, 2005.
- J. Chung, “A distributional version of functional equations and their stabilities,” Nonlinear Analysis: Theory, Methods & Applications, vol. 62, no. 6, pp. 1037–1051, 2005.
- L. Hörmander, The Analysis of Linear Partial Differential Operator I, Springer, Berlin, Germany, 1983.