Abstract
A set of np(≥2)‐cyclic and either continuous or contractive self‐mappings, with at least one of them being contractive, which are defined on a set of subsets of a Banach space, are considered to build a composed self‐mapping of interest. The existence and uniqueness of fixed points and the existence of best proximity points, in the case that the subsets do not intersect, of such composed mappings are investigated by stating and proving ad hoc extensions of several Krasnoselskii‐type theorems.
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