This is an extended version of the talk given on the 10th International Conference on Functional Equations and Inequalities held in September, 2005, in the Mathematical Research and Conference Center of the Polish Academy of Sciences at Będlewo, cf. [A10]. There is presented, first of all, an outline of the history of the ten meetings, organized in Poland by the Institute of Mathematics of the Pedagogical University of Cracow from 1984 to 2005. The article begins with a description of meetings held in Hungary, prior to the ICFEIs, and ends with informations on other conferences and seminars organized by Polish schools of functional equations in the years 1989-2005 (among them, on the International Symposia on Functional Equations: 27 (1989), 34 (1996) and 40 (2002)).

We consider the problem, proposed by the second author (cf. [1]) of solving functional equations stemming from the Steffensen integral inequality (S), which is applicable in actuarial problems, cf. [4]. Imposing some regularity conditions we find solutions of two equations in two variables, one with two and another with three unknown functions.