Jordan $*$-derivations of incidence algebras

Abstract: Let $X$ be a locally finite partially ordered set (poset), $K$ a field of characteristic not 2, and $I(X,K)$ the incidence algebra over $K$. In this paper, we prove that every Jordan $$-derivation of $I(X,K)$ is an inner $$-derivation and a transposed Jordan $$-derivation. Moreover, we demonstrate the existence of Jordan $$-derivations that are not $*$-derivations.