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http://dx.doi.org/10.7468/jksmeb.2011.18.3.231

STABILITY OF TRIGONOMETRIC TYPE FUNCTIONAL EQUATIONS IN RESTRICTED DOMAINS  

Chung, Jae-Young (Department of Mathematics, Kunsan National University)
Publication Information
The Pure and Applied Mathematics / v.18, no.3, 2011 , pp. 231-244 More about this Journal
Abstract
We prove the Hyers-Ulam stability for trigonometric type functional inequalities in restricted domains with time variables. As consequences of the result we obtain asymptotic behaviors of the inequalities and stability of related functional inequalities in almost everywhere sense.
Keywords
Hyers-Ulam stability; additive function; exponential function; trigonometric type functional equation; heat kernel;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 C.G. Park: Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algabras. Bull. Sci. Math. 132 (2008), 87-96.   DOI   ScienceOn
2 J.M. Rassias & M.J. Rassias: On the Ulam stability of Jensen and Jensen type mappings on restricted domains. J. Math. Anal. Appl. 281 (2003), 516-524.   DOI   ScienceOn
3 G.L. Forti: Hyer-Ulam stability of functional equation in several variables. Aequationes Math. 50 (1995), 143-190.   DOI   ScienceOn
4 D.H. Hyers: On the stability of the linear functional equations. Proc. Nat. Acad. Sci. USA 27 (1941), 222-224.   DOI   ScienceOn
5 D.H. Hyers, G. Isac & Th.M. Rassias: Stability of functional equations in several variables. Birkhauser, 1998.
6 S.-M. Jung: Hyers-Ulam stability of Jensen's equation and its application Proc. Amer. Math. Soc. 126 (1998), 3137-3143.   DOI   ScienceOn
7 K.-W. Jun & H.-M. Kim: Stability problem for Jensen-type functional equations of cubic mappings. Acta Mathematica Sinica, English Series 22 (2006), no. 6, 1781-1788.   DOI   ScienceOn
8 G.H. Kim & Y.-H. Lee: Boundedness of approximate trigonometric functional equations. Appled Mathematics Letters 31 (2009), 439-443.
9 J.A. Baker: The stability of cosine functional equation. Proc. Amer. Math. Soc. 80 (1980) 411-416.   DOI   ScienceOn
10 D.G. Bourgin: Class of transformations and bordering transformations. Bull. Amer. Math. Soc. 57 (1951), 223-237.   DOI
11 D.G. Bourgin: Multiplicative transformations. Proc. Nat. Academy Sci. of U.S.A. 36 (1950), 564-570.   DOI   ScienceOn
12 J. Chung: Stability of approximately quadratic Schwartz distributions. Nonlinear Analysis 67 (2007) 175-186.   DOI   ScienceOn
13 J. Chung: A distributional version of functional equations and their stabilities. Nonlinear Analysis 62 (2005), 1037-1051.   DOI   ScienceOn
14 L. Szekelyhidi: The stability of d'Alembert type functional equations. Acta Sci. Math. Szeged. 44 (1982c), 313-320.
15 J. Chang & J. Chung: The stability of the sine and cosine functional equations in Schwartz distributions. Bull. Korean Math. Soc. 45 (2009), no. 1, 87-97.
16 S. Czerwik: Stability of Functional Equations of Ulam-Hyers-Rassias Type. Hadronic Press, Inc., Palm Harbor, Florida, Florida, 2003.
17 T. Aoki: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan 2 (1950), 64-66.   DOI
18 S.M. Ulam: Problems in modern mathematics. Interscience Publ., New York, 1960.
19 S.M. Ulam: A Collection of Mathematical Problems. Science Editions, Wiley, 1968.
20 D.V. Widder: The heat equation. Academic Press, New York, 1975.
21 J.M. Rassias: On Approximation of Approximately Linear Mappings by Linear Mappings. J. Funct. Anal. 46 (1982), 126-130.   DOI
22 I. Tyrala: The stability of d'Alembert's functional equation. Aequationes Math. 69 (2005), 250-256.   DOI   ScienceOn
23 F. Skof: Sull'approssimazione delle applicazioni localmente $\delta$-additive. Atii Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 117 (1983), 377-389.
24 L. Szekelyhidi: The stability of sine and cosine functional equations. Proc. Amer. Math. Soc. 110 (1990), 109-115.   DOI
25 Th.M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 7 (1978), 297-300.
26 K. Ravi & M. Arunkumar: On the Ulam-Gavruta-Rassias stability of the orthogonally Euler-Lagrange type functional equation. Intern. J. Appl. Math. Stat. 7 (2007), 143-156.
27 Th.M. Rassias: On the stability of functional equations in Banach spaces J. Math. Anal. Appl. 251 (2000), 264-284.   DOI   ScienceOn
28 J.M. Rassias: On the Ulam stability of mixed type mappings on restricted domains. J. Math. Anal. Appl. 276 (2002), 747-762.   DOI   ScienceOn