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Diametrically contractive maps and fixed points

Abstract

Contractive maps have nice properties concerning fixed points; a big amount of literature has been devoted to fixed points of nonexpansive maps. The class of shrinking (or strictly contractive) maps is slightly less popular: few specific results on them (not applicable to all nonexpansive maps) appear in the literature and some interesting problems remain open. As an attempt to fill this gap, a condition half way between shrinking and contractive maps has been studied recently. Here we continue the study of the latter notion, solving some open problems concerning these maps.

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Correspondence to Marco Baronti.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Baronti, M., Casini, E. & Papini, P.L. Diametrically contractive maps and fixed points. Fixed Point Theory Appl 2006, 79075 (2006). https://doi.org/10.1155/FPTA/2006/79075

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  • DOI: https://doi.org/10.1155/FPTA/2006/79075

Keywords

  • Open Problem
  • Differential Geometry
  • Specific Result
  • Computational Biology
  • Interesting Problem