  For any class of operators which transform unary total functions in the set
of natural numbers into functions of the same kind, we define what it means for
a real function to be uniformly computable or conditionally computable with
respect to this class. These two computability notions are natural
generalizations of certain notions introduced in a previous paper co-authored
by Andreas Weiermann and in another previous paper by the same authors,
respectively. Under certain weak assumptions about the class in question, we
show that conditional computability is preserved by substitution, that all
conditionally computable real functions are locally uniformly computable, and
that the ones with compact domains are uniformly computable. The introduced
notions have some similarity with the uniform computability and its non-uniform
extension considered by Katrin Tent and Martin Ziegler, however, there are also
essential differences between the conditional computability and the non-uniform
computability in question.
