A method of solving functional equations on convex subsets of linear spaces (Q2481694)

From the author's summary: She introduces a method of solving a wide range of functional equations stemming from mean value theorem. She generalizes some results of \textit{Z. Daróczy} and \textit{Gy. Maksa} [Acta Math. Hung. 68, No. 3, 187--195 (1995; Zbl 0849.39007)] in the spirit of a lemma of \textit{M. Sablik} [Aequationes Math. 60, No. 3, 258--267 (2000; Zbl 0970.39022)]. In what follows the author illustrates the method taking into account two functional equations. One of them is connected with Flett's mean value theorem with which the author dealt in a previous paper [Demonstr. Math. 32, No. 2, 281--286 (1999; Zbl 0955.26003)].