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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...
We study several functional equations, in two variables, that are closely related to the functional equation of permutability. We analyze the hierarchy among these equations, paying a particular attention to their use in Fuzzy Set Theory.
We extend Gajda’s result concerning the stability of the Cauchy’s functional equation to Fréchet’s first polynomial equation.
It is easy to find some discontinuous functions whose iterates are continuous ones, showing that iteration can change discontinuity into continuity. In order to investigate this change and avoid complicated computation, in this paper we classify self-mappings on the compact interval (0, 1) each...
We obtain selections of generalized convex set-valued maps satisfying certain functional equations. As a consequence there follow some results on stability for functional equations on bisymmetric grupoids.
A new bivariate mean is introduced and studied. The mean under discussion is defined as the degenerate case of the completely symmetric elliptic integral of the second kind. Its relationship with the Schwab–Borchardt mean is established. Four particular cases of the mean in question are...
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