ON GENERALIZED (α, β)-DERIVATIONS IN BCI-ALGEBRAS

The notion of generalized (regular) (<TEX>α,\;β</TEX>)-derivations of a BCI-algebra is introduced, some useful examples are discussed, and related properties are investigated. The condition for a generalized (<TEX>α,\;β</TEX>)-derivation to be regular is provided. The concepts of a generalized F-invariant (<TEX>α,\;β</TEX>)-derivation and <TEX>α</TEX>-ideal are introduced, and their relations are discussed. Moreover, some results on regular generalized (<TEX>α,\;β</TEX>)-derivations are proved.