Let $${{\mathfrak {A}}}\, $$ and '$$ be two $$C^*$$ -algebras with identities $$I_{{{\mathfrak }$$ '}$$ , respectively, $$P_1$$ $$P_2 = I_{{{\mathfrak } - P_1$$ nontrivial projections in . In this paper, we study the characterization of multiplicative $$*$$ -Lie–Jordan-type maps, where notion these maps arise here. particular, if $${\mathcal {M}}_{{{\mathfrak is a von Neumann algebra relative $...