Some results on fixed and best proximity points of precyclic self-mappings
type: Item
instance of: scholarly article
title: Some results on fixed and best proximity points of precyclic self-mappings
zbMATH Open document ID: 1397.47006
DOI: 10.1155/2013/310106
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: This paper is devoted to investigating the limit properties of distances and the existence and uniqueness of fixed points, best proximity points and existence, and uniqueness of limit cycles, to which the iterated sequences converge, of single-valued, and the so-called contractive precyclic self-mappings, which are proposed in this paper. Such self-mappings are defined on the union of a finite set of subsets of uniformly convex Banach spaces under generalized contractive conditions. Each point of a subset is mapped either in some point of the same subset or in a point of the adjacent subset. In the general case, the contractive condition of contractive precyclic self-mappings is admitted to be point dependent and it is only formulated on a complete disposal, rather than on each individual subset, while it involves a condition on the number of iterations allowed within each individual subset before switching to its adjacent one. It is also allowed that the distances in-between adjacent subsets can be mutually distinct including the case of potential pairwise intersection for only some of the pairs of adjacent subsets.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 6950611
zbMATH Keywords: Banach space
zbMATH Keywords: contractive precyclic self-mappings
zbMATH Keywords: limit properties of distances
zbMATH Keywords: fixed points
zbMATH Keywords: best proximity points
zbMATH Keywords: limit cycles
Wikidata QID: Q57675073
author: M. De la Sen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/310106
OpenAlex ID: W2089827243
DBLP publication ID: journals/jam/Sen13
description: scientific article; zbMATH DE number 6950611