-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 -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.
"Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings." J. Appl. Math. 2012 (SI03) 1 - 29, 2012. https://doi.org/10.1155/2012/817193