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A linear mapping φ on an algebra A is called a centralizable is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at G is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is a full-centralizable point. We also prove that a point in a von Neumann algebra is a full-derivable point if and only if its central carrier is the unit.doi:10.4134/jkms.j160265 fatcat:df4di7b5gvakllzzcxgx3ewhz4