On p (≥ 2)-Cyclic Contractive Single-Valued Self-Mappings in S-Metric Spaces on the Union of Non-Intersecting Subsets and Some of Their Properties

This paper investigates some properties of contractive p (≥ 2)-cyclic mappings in S-metric spaces on a cyclic disposal of p, in general, non-intersecting nonempty closed subsets of the considered S-metric spaces. The convergence of the distances of points of the sequences between nonempty closed adjacent subsets of the cyclic disposal to the distance in-between such sets is proved. Also, the characterization of the best proximity points is given and it is proved that such best proximity points are also fixed points of the composed self-mappings p-times on themselves. The convergence of the sequences generated by the contractive cyclic self-mappings to best proximity points, one per subset of the cyclic disposal, is proved in the event that the S-metric space is complete. In the most general case, it is not considered that the constants defining the cyclic contraction are less than unity for each pair of adjacent subsets but that the product of all of them is less than unity.