Diagonal fixed points of geometric contractions (Q1624997)

The term ``diagonal fixed point'' in the title refers to fixed points of maps \(S:X\to X\) such that there is a map \(T:X^k\to X\) with \(S(x)=T\underbrace{(x,\dotsc,x)}_{\text{\(k\) times}}\). The author mainly deals with discussing an earlier result by \textit{L. B. Ćirić} and \textit{S. B. Prešić} [Acta Math. Univ. Comen., New Ser. 76, No. 2, 143--147 (2007; Zbl 1164.54030)]. For the entire collection see [Zbl 1403.05004].