On (alpha,beta)-derivations in BCI-algebras

The notion of (regular) (alpha, beta)-derivations of a BCI-algebra X is introduced, some useful examples are discussed, and related properties are investigated. Condition for a (alpha,beta)-derivation to be regular is provided. The concepts of a d(alpha,beta)-invariant (alpha,beta)-derivation and alpha-ideal are introduced, and their relations are discussed. Finally, some results on regular (alpha,beta)-derivations are obtained.