Abstract
The aim of this paper is to study the stability problem of the generalized d'Alembert, Wilson, and Jensen functional equations.
The aim of this paper is to study the stability problem of the generalized d'Alembert, Wilson, and Jensen functional equations.
R. Badora, “On Hyers-Ulam stability of Wilson's functional equation,” Aequationes Mathematicae, vol. 60, no. 3, pp. 211–218, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. Badora and R. Ger, “On some trigonometric functional inequalities,” in Functional Equations—Results and Advances, vol. 3 of Adv. Math. (Dordr.), pp. 3–15, Kluwer Academic, Dordrecht, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. A. Baker, “The stability of the cosine equation,” Proceedings of the American Mathematical Society, vol. 80, no. 3, pp. 411–416, 1980.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. A. Baker, J. Lawrence, and F. Zorzitto, “The stability of the equation ,” Proceedings of the American Mathematical Society, vol. 74, no. 2, pp. 242–246, 1979.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. G. Bourgin, “Approximately isometric and multiplicative transformations on continuous function rings,” Duke Mathematical Journal, vol. 16, no. 2, pp. 385–397, 1949.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. de Place Friis and H. Stetkær, “On the cosine-sine functional equation on groups,” Aequationes Mathematicae, vol. 64, no. 1-2, pp. 145–164, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. Găvruţa, “A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings,” Journal of Mathematical Analysis and Applications, vol. 184, no. 3, pp. 431–436, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetPl. Kannappan, “The functional equation for groups,” Proceedings of the American Mathematical Society, vol. 19, no. 1, pp. 69–74, 1968.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetPl. Kannappan and G. H. Kim, “On the stability of the generalized cosine functional equations,” Annales Academiae Paedagogicae Cracoviensis; Studia Mathematica, vol. 1, pp. 49–58, 2001.
View at: Google ScholarG. H. Kim and S. H. Lee, “Stability of the d'Alembert type functional equations,” Nonlinear Functional Analysis & Applications, vol. 9, no. 4, pp. 593–604, 2004.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC. T. Ng, “Jensen's functional equation on groups. III,” Aequationes Mathematicae, vol. 62, no. 1-2, pp. 143–159, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. Sinopoulos, “Functional equations on semigroups,” Aequationes Mathematicae, vol. 59, no. 3, pp. 255–261, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. Stetkær, “On Jensen's functional equation on groups,” Aequationes Mathematicae, vol. 66, no. 1-2, pp. 100–118, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetL. Székelyhidi, “The stability of d'Alembert-type functional equations,” Acta Scientiarum Mathematicarum (Szeged), vol. 44, no. 3-4, pp. 313–320 (1983), 1982.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. Yang, “The stability of Jensen's equation on amenable locally compact groups,” Results in Mathematics, vol. 46, no. 3-4, pp. 381–388, 2004.
View at: Google Scholar | Zentralblatt MATH | MathSciNet