Nonlinear maps preserving sums of triple products on $\ast $-algebras

Abstract: Let $\mathcal{A}$ and $\mathcal{B}$ be two unital complex $\ast $-algebras such that $\mathcal{A}$ has a nontrivial projection. In this paper, we study the structure of bijective nonlinear maps $\Phi :\mathcal{A}\rightarrow \mathcal{B}$ preserving sum of triple products $\alpha {1} abc+\alpha _{2} a^{}cb^{}+\alpha _{3} ba^{*}c +\alpha _{4} cab^{*}+\alpha _{5} bca+\alpha _{6} cb^{}a^{},$ where the scalars ${\alpha _{k}}{k=1}^{6}$ are complex numbers satisfying some conditions.