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Pasteczka, Paweł
Resultate der Mathematik, 08/2023, Volume: 78, Issue: 4Journal Article
We study the properties of the mean-type mappings M : I p → I p of the form M ( x 1 , ⋯ , x p ) : = ( M 1 ( x α 1 , 1 , ⋯ , x α 1 , d 1 ) , ⋯ , M p ( x α p , 1 , ⋯ , x α p , d p ) ) , where p and d i -s are positive integers, each M i is a d i -variable mean on an interval I ⊂ R , and α i , j -s are elements from { 1 , ⋯ , p } . We show that, under some natural assumption on M i -s, the problem of existing the unique M -invariant mean can be reduced to the ergodicity of the directed graph with vertexes { 1 , ⋯ , p } and edges { ( α i , j , i ) : i , j admissible } .
