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.
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References
Benz W.: The functional equation f(x)f(y)f(z) = f(x) + f(y) + f(z). Aequationes Math. 68, 117–120 (2004)
Davison T.: Report of Meeting 40th International Symposium on Functional Equations. Aequationes Math. 65, 292 (2003)
Kannappan, Pl.: Functional equations and inequalities with applications. In: Monographs in Mathematics. Springer, Heidelberg (2009)
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Hengkrawit, C., Laohakosol, V. & Ponpetch, K. Functional equations characterizing the tangent function over a convex polygon. Aequat. Math. 88, 201–210 (2014). https://doi.org/10.1007/s00010-013-0229-3
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DOI: https://doi.org/10.1007/s00010-013-0229-3