Characterizing approximate global minimizers of the difference of two abstract convex functions with applications

In this paper, we first investigate characterizations of maximal elements of abstract convex functions under a mild condition. Also, we give various characterizations for global "-minimum of the difference of two abstract convex functions and, by using the abstract Rockafellar?s antiderivative, we present the abstract ?-subdifferential of abstract convex functions in terms of their abstract subdifferential. Finally, as an application, a necessary and sufficient condition for global ?-minimum of the difference of two increasing and positively homogeneous (IPH) functions is presented.