On Generalized Jordan Triple (σ,τ)-Higher Derivations in Prime Rings

Let be a ring and let be a Lie ideal of . Suppose that are endomorphisms of , and is the set of all nonnegative integers. A family of mappings is said to be a generalized -higher derivation (resp., generalized Jordan triple -higher derivation) of if there exists a -higher derivation of such that , the identity map on , , and (resp., hold for all and for every If the above conditions hold for all , then is said to be a generalized -higher derivation (resp., generalized Jordan triple -higher derivation) of into . In the present paper it is shown that if is a noncentral square closed Lie ideal of a prime ring of characteristic different from two, then every generalized Jordan triple -higher derivation of into is a generalized -higher derivation of into .