An element a of a semigroup S is called left [right] magnifying if there
exists a proper subset M of S such that S ¼ aM [S ¼ Ma]. Let P(X) be a
semigroup of all partial transformations on a set X under the composition
of maps. A number of results concerning the necessary and sufficient conditions for elements in some interesting generalized semigroups of partial
transformations to be left or right magnifiers are presented.