Problem z nieoczekiwanym, od dawna spóźnionym uogólnieniem : On the convergence of a sequence of iterates

                This problem has long been waiting to be taken into consideration by me. In the book

TEODORESCU Nicolae (coord.), Probleme din Gazeta Matematică: Ediție selectivă și metodologică,

Ed Tehnică, București, 1984

 on page 487, appears problem SC 6 (solved in the same place, on pages 487-488). The author of the problem is mentioned as J. Dieudonné, without clear indications. The solution is given after an article from a Belgian magazine (see « Mathématique et Pédagogie ») number 31 from 1981.

          The same problem is the starting point in an article from MATHEMATYKA, number 3/1987, pages 138-140. The work [1] cited in the bibliography covers the same issue( Problem 173). See the image, taken from another edition:

               Here we discuss a generalization, contained in the Proposition ("TWIERDZENIE") on page 140. You can see a connection between it and Problem 174 in the image, but this does not detract from the value of the article