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Aequationes mathematicae

, Volume 89, Issue 5, pp 1251–1263 | Cite as

On two functional equations with involution on groups related to sine and cosine functions

  • Allison M. Perkins
  • Prasanna K. Sahoo
Article

Abstract

Let G be a group, \({\mathbb{C}}\) be the field of complex numbers, z 0 be any fixed, nonzero element in the center Z(G) of the group G, and \({\sigma : G \to G}\) be an involution. The main goals of this paper are to study the functional equations \({f(x{\sigma}yz_{0}) - f(xyz_{0}) = 2f(x)f(y)}\) and \({f(x{\sigma}yz_{0}) + f(xyz_{0}) = 2f(x)f(y)}\) for all \({x, y \in G}\) and some fixed element z 0 in the center Z(G) of the group G.

Mathematics Subject Classification

39B52 

Keywords

Abelian function involution Kannappan’s functional equation Van Vleck’s functional equation group character 

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References

  1. 1.
    Corovei I.: The cosine functional equation for nilpotent groups. Aequationes Math. 15, 99–106 (1977)CrossRefMathSciNetMATHGoogle Scholar
  2. 2.
    Etigson L.B.: A cosine functional equation with restricted arguments. Can. Math. Bull. 17(4), 505–509 (1974)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Kannappan Pl.: A functional equation for the cosine. Can. Math. Bull. 2, 495–498 (1968)CrossRefGoogle Scholar
  4. 4.
    Kannappan Pl.: Functional Equations and Inequalities with Applications. Springer, New York (2009)CrossRefMATHGoogle Scholar
  5. 5.
    Sahoo P.K., Kannappan Pl.: Introduction to Functional Equations. CRC Press, Boca Raton (2011)MATHGoogle Scholar
  6. 6.
    Perkins, A.M., Sahoo, P.K.: A functional equation with involution related to the cosine function (2014, submitted)Google Scholar
  7. 7.
    Sahoo, P.K.: A functional equation with restricted argument related to cosine function (2014, submitted)Google Scholar
  8. 8.
    Stetkaer H.: Functional Equations on Groups. World Scientific Publishing Co., Singapore (2013)CrossRefMATHGoogle Scholar
  9. 9.
    Van Vleck E.B.: A functional equation for the sine. Ann. Math. 7, 161–165 (1910)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of LouisvilleLouisvilleUSA

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