Mutually odd functions

The floor of a real number x is the largest integer n ≤ x, written ⌊x⌋.

The ceiling of a real number x is the smallest integer n ≥ x, written ⌈x⌉.

The floor and ceiling have the following symmetric relationship:

⌊-x⌋ = -⌈x⌉ ⌈-x⌉ = -⌊x⌋

The floor and ceiling functions are not odd, but as a pair they satisfy a generalized parity condition:

f(-x) = -g(x) g(-x) = -f(x)

If the functions f and g are equal, then each is an odd function. But in general f and g could be different, as with floor and ceiling.

Is there an established name for this sort of relation? I thought of “mutually odd” because it reminds me of mutual recursion.

Can you think of other examples of mutually odd functions?