Abstract
In this paper we study the regularity of inside (or outside) (theta,phi)-derivations in BCI-algebras X and prove that let d((theta,phi)) : X -> X be an inside (theta,phi)-derivation of X. If there exists a is an element of X such that d((theta,phi)) (x) * theta(a) = 0, then d((theta,phi)) is regular for all x is an element of X. It is also shown that if X is a BCK-algebra, then every inside (or outside) (theta,phi)-d erivation of X is regular. Further more the concepts of theta-ideal, phi-ideal and invariant inside (or outside) (theta,phi)-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If d((theta,phi)) : X -> X is an outside (theta,phi)-derivation of X,then d(theta,phi) is regular if and only if every theta-ideal of X is d((theta,phi))-invariant.