We present a further study on fixed point theory for the so called iterated nonexpansive
mappings, that is, mappings which are nonexpansive along the orbits. They are a direct
generalization of the contraction type maps studied by Rheinboldt in the late sixties of the last
century.
This is a wide class of nonlinear mappings including several families of generalized
nonexpansive mappings appearing in the recent litherature.
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