On rough convergence in amenable semigroups and some properties

The authors of the present paper, firstly, investigated relations between the notions of rough convergence and classical convergence, and studied on some properties of the rough convergence notion which the set of rough limit points and rough cluster points of a sequence of functions defined on amenable semigroups. Then, they examined the dependence of r-limit LIM^r f of a fixed function f ∈ G on varying parameter r.