In this paper, we continue the study on the ideal analogues of several
variations of the Hurewicz property introduced by Das et al. [4, 6, 7] for
example, the I-Hurewicz (IH), the star I-Hurewicz (SIH), the weakly
I-Hurewicz (WIH) and the weakly star-I-Hurewicz (WSIH). It is shown that
several implications in the relationship diagram of their concepts are
reversible under certain conditions, for instance; (1) If a paracompact
Hausdorff space has the WSIHproperty, then it has theWIHproperty. (2) If the
complement of dense set has the IHproperty, then theWIHproperty implies the
IHproperty and (3) If the complement of dense set has the SIH property, then
the WSIH property implies the SIH property. In addition, we introduce the
ideal analogues of some new variations of the Hurewicz property called the
mildly I-Hurewicz and the star K-I-Hurewicz properties and explore their
relationships with other variants of the I-Hurewicz property. We also study
the preservation properties under certain mappings.