The author studies the functional equation \((1-K)\) \(T(X,X) + KT^* (X,X) = X\), where \(K\) is a given constant in \((0,1)\), \(X\) is a variable in \([0,1]\), \(T\) is a nonstrict Archimedean \(t\)-norm in \([0,1]\) to be found, \(T^* (X,Y) = n_ T(T(n_ T (X),\;n_ T(Y))\) and \(n_ T (X) = t^{- 1} (1 - t(X))\), where \(t\) is the additive generator of \(T\). By doing this, some interesting relations with De Rham's function are obtained.