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ON THE SUPERSTABILITY OF SOME PEXIDER TYPE FUNCTIONAL EQUATION II  

Kim, Gwang-Hui (Department of Mathematics, Kangnam University)
Publication Information
The Pure and Applied Mathematics / v.17, no.4, 2010 , pp. 397-411 More about this Journal
Abstract
In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.
Keywords
stability, superstability; functional equation; d'Alembert equation; (hyperbolic) cosine functional equation;
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1 J.A. Baker: The stability of the cosine equation. Proc. Amer. Math. Soc. 80 (1980), 411-416.   DOI   ScienceOn
2 G.H. Kim: On the Stability of the Pexiderized trigonometric functional equation. Appl. Math. Comput. 203 (2008), 99-105   DOI   ScienceOn
3 G.H. Kim: On the Stability of trigonometric functional equations, Ad. Diff. Eq., Vol 2007, Article ID 90405, (2007).
4 P. Gavruta: On the stability of some functional equations. in : Th.M. Rassias and J. Tabor, Stability of mappings of Hyers-Ulam type, Hadronic Press, 1994, pp. 93-98.
5 G.H. Kim: On the stability of Mixed Trigonometric Functional Equations. Banach J. Math. Anal. 1 (2007), no. 2, 227-236.   DOI
6 G.H. Kim: On the Stability of the generalized sine functional equations. Acta Math. Sin., Engl. Ser. 25 (2009), 29-38.   DOI   ScienceOn
7 PI. Kannappan & G.H. Kim: On the stability of the generalized cosine functional equations. Ann. Acad. Pedagog. Crac. Stud. Math. 1 (2001), 49-58.
8 PI. Kannappan: The functional equation f(xy)+ f($xy^{-1}$) = 2f(x)f(y) for groups. Proc. Amer. Math. Soc. 19 (1968), 69-74.
9 PI. Kannappan: Functional equations and inequailitis with applications. Springer, 2009.
10 D.H. Hyers: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. 27 (1941), 222-224.   DOI   ScienceOn
11 G.H. Kim & Y.H. Lee: Boundedness of approximate trigonometric functional equations. Appl. Math. Lett. 331 (2009), 439-443.
12 J.A. Baker, J. Lawrence & F. Zorzitto: The stability of the equation f(x+y) = f(x)f(y). Proc. Amer. Math. Soc. 74 (1979), 242-246.
13 D.G. Bourgin: Approximately isometric and multiplicative transformations on continuous function rings. Duke Math. J. 16 (1949), 385-397.   DOI
14 S.M. Ulam: "Problems in Modern Mathematics" Chap. VI, Science editions, Wiley, New York, 1964
15 R. Badora: On the stability of cosine functional equation. Rocznik Naukowo-Dydak. Prace Mat. 15 (1998), 1-14.
16 Th.M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72 (1978), 297-300.   DOI   ScienceOn
17 R. Badora & R. Ger: On some trigonometric functional inequalities. Functional Equations-Results and Advances (2002), 3-15.
18 J. Aczel: Lectures on Functional Equations and their Applications. Academic Press, New York, 1966.
19 J. Aczel & J. Dhombres: Functional Equations in Several Variables. Cambridge University Press, Cambridge, 1988.
20 G.H. Kim & Sever S. Dragomir: On the stability of generalized d'Alembert and Jensen functional equation. Intern. J. Math. & Math. Sci. 2006 Article ID 43185(2006), 1-12.
21 P.W. Cholewa: The stability of the sine equation. Proc. Amer. Math. Soc. 88 (1983), 631-634.   DOI   ScienceOn
22 G.H. Kim & Y.H. Lee: The superstability of the Pexider type trigonometric functional equation. Aust. J. Math. Anal., preprint
23 G.H. Kim: The stability of the d'Alembert and Jensen type functional equations. J. Math. Anal. Appl. 325 (2007), 237-248.   DOI   ScienceOn
24 G.H. Kim: A stability of the generalized sine functional equations. J. Math. Anal. Appl. 331 (2007), 886-894.   DOI   ScienceOn