DOI: 10.5176/2251-1911_CMCGS15
Authors: Manuel De La Sen
Abstract: This paper discusses a more general contractive condition for a class of extended 2-cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. If the space is uniformly convex and the subsets are non-empty, closed and convex then all the iterates converge to a unique closed limiting finite sequence which contains the best proximity points of adjacent subsets and reduces to a unique fixed point if all such subsets intersect.
Keywords: Pseudontractions, cyclic-self-maps, best proximity points , fixed points.
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