On the Structure of Minimal Sets of Relatively Nonexpansive Mappings

• Published in: Numerical functional analysis and optimization Vol. 34; no. 8; pp. 845 - 860
• Main Authors: Espínola, Rafa, Gabeleh, Moosa
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 03.08.2013
• Subjects: Best proximity point; Fixed point; Functional analysis; Mapping; Optimization; Property UC; Proximal normal structure; Relatively non-expansive mapping

In this article, we study the structure of minimal sets of relatively non-expansive mappings. We consider the cyclic and the noncyclic cases and show that results alike to the celebrated Goebel-Karlovitz lemma for non-expansive self-mappings can be obtained for relatively non-expansive mappings.