Abstract and Applied Analysis

On a Cubic Equation and a Jensen-Quadratic Equation

Jae-Hyeong Bae and Won-Gil Park

Full-text: Open access

Abstract

We obtain the general solutions of the cubic functional equation 3 [ g ( x + y ) + g ( x y ) + 6 g ( x ) ] = 2 g ( 2 x + y ) + 2 g ( 2 x y ) + g ( x y ) + g ( x + y ) + 6 g ( x ) and the Jensen-quadratic functional equation f ( ( x + y ) / 2 , z + w ) + f ( ( x + y ) / 2 , z w ) = f ( x , z ) + f ( x , w ) + f ( y , z ) + f ( y , w ) .

Article information

Source
Abstr. Appl. Anal., Volume 2007 (2007), Article ID 45179, 10 pages.

Dates
First available in Project Euclid: 27 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1204126606

Digital Object Identifier
doi:10.1155/2007/45179

Mathematical Reviews number (MathSciNet)
MR2365815

Zentralblatt MATH identifier
1156.39014

Citation

Bae, Jae-Hyeong; Park, Won-Gil. On a Cubic Equation and a Jensen-Quadratic Equation. Abstr. Appl. Anal. 2007 (2007), Article ID 45179, 10 pages. doi:10.1155/2007/45179. https://projecteuclid.org/euclid.aaa/1204126606


Export citation

References

  • S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, USA, 2002.
  • 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.
  • S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, Fla, USA, 2001.
  • Th. M. Rassias, Functional Equations and Inequalities, vol. 518 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
  • 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.
  • 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.