Characterizing Jordan Higher Centralizers on Triangular Rings through Zero Product

In this paper , we prove that if T is a 2-torsion free triangular ring and φ= (φi)i∈N be a family of additive mapping φi:T→T then φ satisfying Xφi (Y)+φi (Y)X=0 ∀ i∈N whenever X,Y∈T,XY=YX=0 ifand only if φ is a higher centralizer which is means that φ is Jordan higher centralizer on 2-torsion free triangular ring if and only if φ is a higher centralizer and also we prove that if φ=(φi)i∈N be a family of additive mapping φi:T→T satisfying the relation φ_n (XYX)=∑_(i=1)^n X φi (Y)X ∀ X,Y∈T, Then φ is a higher centralizer.