On generalized $f$-derivations of lattice implication algebras

Abstract

In this paper, we introduce the notion of generalized $f$-derivation of lattice implication algebra and investigate some related properties. Also, we prove that if $D$ is a generalized $f$-derivation associated with an $f$-derivation $d$ of $L,$ then $D(x\to y)=f(x)\to D(y)$ for all $x, y\in L.$