Duly

(adv.) In a due, fit, or becoming manner; as it (anything) ought to be; properly; regularly.

Thesaurus Entries

accordingly, appropriately, as is proper, as is right, by right, by rights, condignly, correctly, deservedly, disinterestedly, dispassionately, equally, equitably, evenly, fair, fairly, fittingly, impartially, impersonally, in all conscience, in reason, inequity, injustice, justifiably, justifiedly, justly, meetly, on time, properly, punctually, right, rightfully, rightly, suitably, upon even terms, warrantably, warrantedly, without distinction