Verb tenses question

I have been looking all over for this and couldn't find it--I figured maybe
someone here would know.

I need a name for the verb tense that denotes an action that is beginning,
in the same way that the 'perfect' tense denotes an action that has finished
and the 'progressive' tense denotes one that is continuing.

In English we don't have it and use forms like
     'I was going to eat',
     'I am about to eat',
     'I will be getting ready to eat'

The only example I know offhand is Esperanto's -onta, which I also cannot
find a name for.

     *Muke!