Abstract
Motivated by Dar and Ali's [9] elegant work's, the goal of the paper is to study nth power *-property in rings with involution and its related problems. In fact, the main result of this paper gives conditions which ensure that an additive map d : R -> R satisfying nth power *-property must be X-inner. As an application, we characterize additive map F : R -> R such that F(x(n)) = F(x)(x*)(n-1) + Sigma(n=1)(i=1) x(i)d(x)(x*)(n-i-1) for all x is an element of R: where d : R -> R is an additive map satisfying nth power *-property. These results provide the affirmative answer to the open problem (see Problem 3.3 [9]).