On I_{σ}-convergence of folner sequence on amenable semigroups

Abstract

In this paper, the concepts of-uniform density of subsetsAof the setof positive integers and corresponding-convergence of functions defined on discrete countable amenable semigroups were introduced. Furthermore, for any Folner sequenceinclusion relations between-convergence and invariant convergence also-convergence andVp-convergence were given. Weintroduce the concept of-statisticalconvergence and-lacunary statisticalconvergence of functions defined on discrete countableamenable semigroups. In addition to these definitions, we give some inclusion theorems. Also, we make a new approach to the notionsofV-summability,-convergence and-statistical convergence of Folner sequences by using ideals and introduce new notions,namely,-V-summability,--statisticalconvergence of Folner sequences. We mainly examine the relation between these twomethods as also the relation between-statistical convergence and--statistical convergence of Folner sequences introduced bythe author recently.