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Aequationes mathematicae

, Volume 88, Issue 3, pp 201–210 | Cite as

Functional equations characterizing the tangent function over a convex polygon

  • Charinthip Hengkrawit
  • Vichian Laohakosol
  • Kanet Ponpetch
Article

Abstract

In 2004, Benz, affirming an earlier result of Davison, proved that for the three angles x,y,z of a non-degenerate triangle, the functional equation f(x)f(y)f(z) = f(x) + f(y) + f(z) characterizes the tangent function. We generalize this result by exhibiting a functional equation, with n parameters representing the angles of a non-degenerate convex n-gon, which characterizes the tangent function.

Mathematics Subject Classification (2000)

39B05 39B22 

Keywords

Functional equation tangent function non-degenerate convex n-gon 

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References

  1. 1.
    Benz W.: The functional equation f(x)f(y)f(z) = f(x) + f(y) + f(z). Aequationes Math. 68, 117–120 (2004)MATHMathSciNetGoogle Scholar
  2. 2.
    Davison T.: Report of Meeting 40th International Symposium on Functional Equations. Aequationes Math. 65, 292 (2003)Google Scholar
  3. 3.
    Kannappan, Pl.: Functional equations and inequalities with applications. In: Monographs in Mathematics. Springer, Heidelberg (2009)Google Scholar
  4. 4.
    Aczél J., Dhombres J.: Functional Equations in Several Variables. Cambridge University Press, Cambridge (1989)CrossRefMATHGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Charinthip Hengkrawit
    • 1
  • Vichian Laohakosol
    • 2
    • 3
  • Kanet Ponpetch
    • 1
  1. 1.Department of Mathematics and Statistics, Faculty of Science and TechnologyThammasat UniversityPhatumthaniThailand
  2. 2.Department of MathematicsKasetsart UniversityBangkokThailand
  3. 3.Centre of Excellence in MathematicsCHEBangkokThailand

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