Abstract
In the present paper, we discuss the commutativity of semi prime rings. Further, using this result, we establish that if U is a semiprime Banach algebra, and H-1 and H-2 are nonvoid open subsets of U which admit a continuous derivation d : U -> U such that d(x(m)) o d(y(n)) +/- x(m) o y(n) = 0 for all x is an element of H-1 and y is an element of H-2, where m,n are no longer fixed but they depend on the pair of elements x and y, then U is commutative.