Browse > Article
http://dx.doi.org/10.4134/BKMS.2009.46.1.087

THE STABILITY OF THE SINE AND COSINE FUNCTIONAL EQUATIONS IN SCHWARTZ DISTRIBUTIONS  

Chang, Jeong-Wook (DEPARTMENT OF MATHEMATICS KUNSAN NATIONAL UNIVERSITY)
Chung, Jae-Young (DEPARTMENT OF MATHEMATICS KUNSAN NATIONAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.1, 2009 , pp. 87-97 More about this Journal
Abstract
We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.
Keywords
Hyers-Ulam stability; trigonometric functional equation; distributions; Fourier hyperfunctions; Gelfand generalized functions; heat kernel;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
1 J. Aczel, Lectures on Functional Equations and Their Applications, Mathematics in Science and Engineering, Vol. 19 Academic Press, New York-London, 1966.
2 J. Aczel and J. Dhombres, Functional Equations in Several Variables, Encyclopedia of Mathematics and its Applications, 31. Cambridge University Press, Cambridge, 1989.
3 J. A. Baker, On a functional equation of Acz´el and Chung, Aequationes Math. 46 (1993), no. 1-2, 99-111.   DOI
4 J.-Y. Chung, A distributional version of functional equations and their stabilities, Nonlinear Anal. 62 (2005), no. 6, 1037-1051.   DOI   ScienceOn
5 I. M. Gelfand and G. E. Shilov, Generalized Functions. Vol. 2, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1968.
6 L. Hormander, The Analysis of Linear Partial Differential Operators. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 256. Springer-Verlag, Berlin, 1983.
7 J. A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), no. 3, 411-416.   DOI   ScienceOn
8 Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 264-284.   DOI   ScienceOn
9 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300.   DOI   ScienceOn
10 L. Schwartz, Theorie des distributions, Hermann, Paris, 1966.
11 J. A. Baker, Functional equations, tempered distributions and Fourier transforms, Trans. Amer. Math. Soc. 315 (1989), no. 1, 57-68.   DOI   ScienceOn
12 L. Szekelyhidi, The stability of the sine and cosine functional equations, Proc. Amer. Math. Soc. 110 (1990), no. 1, 109-115.   DOI
13 J. A. Baker, Distributional methods for functional equations, Aequationes Math. 62 (2001), no. 1-2, 136-142.   DOI
14 D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224.   DOI   ScienceOn
15 D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser Boston, Inc., Boston, MA, 1998.
16 D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153.   DOI
17 S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Inc., Palm Harbor, FL, 2001.
18 L. Szekelyhidi, The stability of d'Alembert type functional equations, Acta Sci. Math. (Szeged) 44 (1982), no. 3-4, 313-320.
19 I. Tyrala, The stability of d'Alembert's functional equation, Aequationes Math. 69 (2005), no. 3, 250-256.   DOI
20 S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York-London, 1960.
21 D. V. Widder, The Heat Equation, Academic Press, New York, 1975.