Maps of \(*\)-derivation-type on sums of triple products on \(*\)-algebras

Abstract

Let \(\mathcal {M}\) be a unital prime complex \(*\)-algebra having a non-trivial projection. In this paper, we proved that every \(*\)-derivation-type map \(\Phi :\mathcal {M}\rightarrow \mathcal {M}\) on sum of triple products \(\alpha _{1} abc+\alpha _{2} a^{*}cb^{*}+\alpha _{3} bac +\alpha _{4} ca^{*}b^{*}+\alpha _{5} bca+\alpha _{6} cb^{*}a^{*},\) where the scalars \(\{\alpha _{k}\}_{k=1}^{6}\) are rational numbers satisfying some conditions, is an additive \(*\)-derivation. An application of the main result is also presented.