(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The intention of the current research is to define the concept of (α,*)-derivations on ring R, where α is an automorphism of R and * represents involution on R. We obtain some commutativity theorems in case of prime ring by utilizing the role of α and *. We will also discuss the proofs of theorems in case of non-commutative prime ring and under which condition generalized (α,*)-derivation behaves like an α-centralizers. Suitable examples are given in favor of introduced concept.