A note on Q-order of convergence

To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. ii new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-order (at least) by showing the existence of a unique real number q is an element of [1, +infinity] such that either exact Q-order, exact Q-superorder, or exact Q-suborder q of convergence holds.