Mappings preserving sum of products α1ab + α2ba + α3ba (resp., Α1ab + α2ba + α3ab) on -algebras

Let A and B be two unital prime complex *-algebras such that A has a nontrivial projection. In this paper, we study the structure of the bijective mappings ? ? A ? B preserving sum of products ?1ab* + ?2b*a + ?3ba* (resp., ?1ab* + ?2b*a + ?3a*b), where the scalars {?k}3k =1 are rational numbers satisfying some conditions.