A note on a uniqueness theorem for the second-derivative test of Qi

Qi [3] has given a theorem which guarantees the existence and uniqueness of a zero x* of a function f: Rn -> Rn in a bounded closed rectangular convex set [x] is contained in Rn under more general sufficient conditions than those described by Moore [1] and has defined an operator (the so-called second-derivative operator) together with a test, involving the second-derivative operator, for the existence but not the uniqueness of a zero x* of f in [x]. The purpose of the present note is to correct the proof of a theorem of Wolfe [4] containing sufficients conditions for the uniqueness if x* using the second-derivative operator.