Abstract
In this paper, we present a further study of iterated nonexpansive mappings, that is, mappings which are nonexpansive along the orbits. This is a wide class of nonlinear mappings including many generalized nonexpansive mappings, such as Suzuki (C)-type generalized nonexpansive mappings and, among others, mappings satisfying the so-called condition (B). In some cases, as for Suzuki (C)-type generalized nonexpansive mappings, the existence of a fixed point is known in the setting of Banach spaces with normal structure. We prove that the same is true for many other classes of iterated nonexpansive mappings.
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