Abstract :
In this paper, it is proved that a locally Lipschitzian function has a PHR iteration
function or a QS iteration function if and only if it is pseudo-regular, and a locally
Lipschitzian function has a positive homogeneous PHR iteration function or a
positive homogeneous QS iteration function if and only if it is continuously
differentiable. In addition, we also give the computable PHR iteration functions or
QS iteration functions for a piece-wise smooth function and a subsmooth function,
respectively.
