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On a cubic equation and a Jensen-quadratic equation. (English) Zbl 1156.39014

The authors introduce a cubic functional equation as well as a Jensen-quadratic functional equation and then they obtain their corresponding equations. The considered individual theorems are proved in a clear and rigorous manner.

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
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References:

[1] S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, USA, 2002. · Zbl 1011.39019
[2] D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, vol. 34 of Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser, Boston, Mass, USA, 1998. · Zbl 0907.39025
[3] S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, Fla, USA, 2001. · Zbl 0980.39024
[4] Th. M. Rassias, Functional Equations and Inequalities, vol. 518 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000. · Zbl 0945.00010
[5] J. Aczél and J. Dhombres, Functional Equations in Several Variables, vol. 31 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 1989. · Zbl 0685.39006
[6] K.-W. Jun and H.-M. Kim, “The generalized Hyers-Ulam-Rassias stability of a cubic functional equation,” Journal of Mathematical Analysis and Applications, vol. 274, no. 2, pp. 867-878, 2002. · Zbl 1021.39014 · doi:10.1016/S0022-247X(02)00415-8
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