Reiter's condition for amenable hypergroups (Q548085)

The authors introduce variants of Reiter's condition \((P_r)\) for \(r\geq1\) for general hypergroups with left Haar measure by using powers and roots of the involved functions. For groups, the new conditions are trivially equivalent to the classical ones, but this is usually not the case for hypergroups, as here usually \(T_x(fg)\neq T_xf\cdot T_xg\) holds. The authors derive several nontrivial connections between these notions, but, in the opinion of the reviewer, the results have no clear impact to other important and basic open problems in hypergroup theory.