Is there a name for the class of operations containing prefix, suffix, etc? I'm currently doing some research on operations on languages, specifically prefix, suffix, infix and outfix.

For example, for a language $L$, the prefix set of $L$ is: 

$pref(L) = \{x \mid xy \in L, y \in \Sigma^* \}$

Infix is

$inf(L) = \{w \mid xwy \in L, x,y \in \Sigma^* \}$

and outfix is:

$outf(L) = \{xy \mid xwy \in L, w \in \Sigma^* \}$

I'm wondering, is there a name for the "class" of operations which contains all of these? I think I might have seen "bitfix" used in a paper somewhere, but it seems to mean something different.
In natural languages, at least, the term is affix.