The generalized dual Gottlieb sets

We define and study a generalized dual Gottlieb set between the dual Gottlieb set and the homotopy set. We find some conditions for which two of them are equal and we also give an example such that none of them are equal. We can obtain a property of the generalized dual Gottlieb group about a homotopically trivial cofibration, which is a stronger dual result than Lee and Wooʹs. We can also obtain a generalization of Halbhavi and Varadarajanʹs result about extending the dual Gottlieb group.