User blog comment:Rgetar/Higher weakly inaccessible and weakly Mahlo cardinals/@comment-28606698-20200106214759

I think the simplest definition of Mahlo cardinals is the follows:

An ordinal π is weakly Mahlo iff every normal function on it has a regular fixed point,

in other words, for every normal function f:π →π from ordinals to ordinals, less than π, there exist a regular cardinal κ< π such that f(κ)=κ and f(α)< κ for all α< κ.

Also:

π is uncountable regular cardinal iff every normal function f:π → π has a fixed point.

π is strongly Mahlo iff every normal function f:π → π has a strongly inaccessible fixed point.