Help with Linear recurrence relation with balanced partition In my slides for my algorithms class, I have a method of finding complexity of recursive functions called Recurrence Relation with "partizione bilanciata" which means "balanced partition".

My course is in Italian and looking online in English I could not find any trace of this method, I know of the recursive tree, induction and master theorem. 

Has anyone an idea of how this is called in English? I don't like studying in Italian and I do not understand those pdfs.

I'm attaching some images of the formulas.





What exactly "balanced partition" mean, does it have something to do with for example Quick Sort, when you choose a middle pivot and the partitions are equal in size, which means it's balanced ?

Is it the same as master theorem written maybe in a different way?
I can see the form of the recurrence relation is different than the master theorem:



The master theorem has $f(n)$ instead of $cn^\beta$.
Looks like I learned it by myself in a different way than my teacher teaches it, and that is why I never heard of "balanced partition".

Apparently it means that a problem is divided in more sub problems (kind of like quick sort as I said), and when we have this condition where T(n/b) and b>=2, we use the "balanced partition" method.

I learned it in a different way, by getting Theta as f(n) and looking for p and k, where Theta(n^k * log^p(n)) , after that I have different cases, like in the following picture, my teacher teaches in a different way and that is why i got confused, because in English there is no "balanced partition" therm.