Advertisement

Solution of a general pexiderized permanental functional equation

  • Vichian Laohakosol
  • Wuttichai Suriyacharoen
Article
  • 26 Downloads

Abstract

A general solution of the pexiderized functional equation
$$\begin{aligned} f(ux+vy,uy-vx, zw)=g(x,y,z)\;h(u,v,w) \end{aligned}$$
is determined without any regularity assumptions. This equation arises from identities satisfied by the permanent of certain symmetric matrices. The solution so obtained are applied to deduce a number of existing related functional equations.

Keywords

Permanent multiplicative function exponential function functional equation 

2010 Mathematics Subject Classification

39B22 15A15 

References

  1. 1.
    Choi C K, Kim J and Lee B, Stability of two functional equations arising from determinant of matrices, Commun. Korean Math. Soc. 31 (2016) 495–505MathSciNetCrossRefGoogle Scholar
  2. 2.
    Chung J K and Sahoo P K, General solution of some functional equations related to the determinant of symmetric matrices, Demonstratio Math. 35 (2002) 539–544MathSciNetzbMATHGoogle Scholar
  3. 3.
    Chung J and Chang J, On two functional equations originating from number theory, Proc. Indian Acad. Sci. (Math. Sci.) 125 (2014) 563–572MathSciNetCrossRefGoogle Scholar
  4. 4.
    Houston K B and Sahoo P K, On a functional equation related to the determinant of symmetric two-by-two matrices, Sarajevo J. Math. 3 (2007) 1–12MathSciNetzbMATHGoogle Scholar
  5. 5.
    Houston K B and Sahoo P K, Some functional equations originating from number theory, Proc. Indian Acad. Sci. (Math. Sci.) 113 (2003) 91–98MathSciNetCrossRefGoogle Scholar
  6. 6.
    Jung S M and Bae J H, General solution of some functional equations related to the determinant of symmetric matrices, Demonstratio Math. 35 (2002) 539–544MathSciNetGoogle Scholar
  7. 7.
    Kannappan Pl, Functional Equations and Inequalities with Applications (2009) (Springer, Dordrecht)Google Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKasetsart UniversityBangkokThailand
  2. 2.Department of Mathematics and Statistics, Faculty of Science and TechnologyThammasat UniversityKhlong LuangThailand

Personalised recommendations