We investigate the duality between call-by-name recursion and call-by-value iteration on the -calculi. The duality between call-by-name and call-by-value was first studied by Filinski, and Selinger has studied the category-theoretic duality on the models of the call-by-name -calculus and the call-by-value one. We extend the call-by-name -calculus and the call-by-value one with a fixed-point operator and an iteration operator, respectively. We show that the dual translations constructed by Selinger can be expanded into our extended -calculi, and we also discuss their implications to practical applications.