Jordan Higher Derivable Mappings on Rings. (18th November 2014) - Ashraf, Mohammad; Parveen, Nazia
Abstract : Let R be a ring. We say that a family of maps D = d n n ∈ N is a Jordan higher derivable map (without assumption of additivity) on R if d 0 = I R (the identity map on R ) and d n ( a b + b a ) = ∑ p + q = n ‍ d p ( a ) d q ( b ) + ∑ p + q = n ‍ d p ( b ) d q ( a ) hold for all a, b ∈ R and for each n ∈ N . In this paper, we show that every Jordan higher derivable map on a ring under certain assumptions becomes a higher derivation. As its application, we get that every Jordan higher derivable map on Banach algebra is an additive higher derivation.