Abstract
p(≥2)‐cyclic and contractive self‐mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p‐cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self‐mappings in order to be Kannan self‐mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self‐mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.
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