NOTES ON THE SUPERSTABILITY OF DALEMBERT TYPE FUNCTIONAL EQUATIONS

Title & Authors
NOTES ON THE SUPERSTABILITY OF DALEMBERT TYPE FUNCTIONAL EQUATIONS
Cao, Peng; Xu, Bing;

Abstract
In this paper we will investigate the superstability of the generalized dAlembert type functional equations ${\sum}^m_{i Keywords dAlembert functional equation;superstability;cosine function; Language English Cited by 1. On the superstability of the pexider type generalized trigonometric functional equations, Acta Mathematica Scientia, 2014, 34, 6, 1749 References 1. R. Badora and R. Ger, On some trigonometric functional inequalities, Functional equations-results and advances, 3–15, Adv. Math. (Dordr.), 3, Kluwer Acad. Publ., Dordrecht, 2002 2. J. A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), no. 3, 411–416 3. J. Baker, J. Lawrence, and F. Zorzitto, The stability of the equation f(x+y) = f(x)f(y), Proc. Amer. Math. Soc. 74 (1979), no. 2, 242–246 4. J. D'Alembert, Memoire sur les principes de la mecanique, Hist. Acad. Sci. (1769), 278–286 5. D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and their Applications, 34. Birkhauser Boston, Inc., Boston, MA, 1998 6. S.-M. Jung, On an asymptotic behavior of exponential functional equation, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 2, 583–586 7. Pl. Kannappan, The functional equation f(xy)+$f(xy^{-1})\$ = 2f(x)f(y) for groups, Proc. Amer. Math. Soc. 19 (1968), no. 1, 69–74

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