A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings

• Autorzy: Sławomir Borzdyński , Andrzej Wiśnicki
• Języki publikacji: EN

Abstrakty

EN

It is shown that if 𝓢 is a commuting family of weak* continuous nonexpansive mappings acting on a weak* compact convex subset C of the dual Banach space E, then the set of common fixed points of 𝓢 is a nonempty nonexpansive retract of C. This partially solves an open problem in metric fixed point theory in the case of commutative semigroups.

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 46B20: Geometry and structure of normed linear spaces
• 47H10: Fixed-point theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 225
• Numer: 2
• Strony: 173-181

Daty

wydano

2014

Twórcy

autor

Sławomir Borzdyński

• Department of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin, Poland

autor

Andrzej Wiśnicki

• Department of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin, Poland

Identyfikatory

DOI

10.4064/sm225-2-4