  The notion of f-derivations was introduced by Beidar and Fong to unify
several kinds of linear maps including derivations, Lie derivations and Jordan
derivations. In this paper we introduce the notion of f-biderivations as a
natural "biderivation" counterpart of the notion of "f-derivations". We first
show, under some conditions, that any f-derivation is a Jordan biderivation.
Then, we turn to study f-biderivations of a unital algebra with an idempotent.
Our second main result shows, under some conditions, that every Jordan
biderivation can be written as a sum of a biderivation, an antibiderivation and
an extremal biderivation. As a consequence we show that every Jordan
biderivation on a triangular algebra is a biderivation.
