An overview on the Prus-Szczepanik condition

Author:

Hernández-Linares Carlos A,Llorens-Fuster Enrique,Mazcuñán-Navarro Eva M,Muñiz-Pérez Omar

Abstract

Abstract In 2005 Prus and Sczcepanik introduced a large class of Banach spaces with the fixed point property for nonexpansive mappings. We say that this class satisfies the PSz condition. Checking that a given Banach space belongs to this class is not an easy task. Here we study the relationship between the PSz condition and other well-known geometrical properties of Banach spaces, and we give easier sufficient conditions for a Banach space to satisfy it.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Geometry and Topology

Reference21 articles.

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3. Prus S, Szczepanik M: Nearly uniformly noncreasy Banach spaces. J. Math. Anal. Appl. 2005, 307: 255–273. 10.1016/j.jmaa.2004.10.049

4. Llorens-Fuster E, Muñiz-Pérez O: Some relationships between sufficient conditions for the fixed point property. Fixed Point Theory 2013, 14: 125–140.

5. Betiuk-Pilarska A, Wiśnicki A: On the Suzuki nonexpansive-type mappings. Ann. Funct. Anal. 2013, 4: 72–86.

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1. The fixed point property for some generalized nonexpansive mappings and renormings;Journal of Mathematical Analysis and Applications;2015-09

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