The τ-fixed point property for left reversible semigroups

In this article we use the generalized Gossez-Lami Dozo property and the Opial condition to study the fixed point property for left reversible semigroups in separable Banach spaces. As a consequence, some previous results will be deduced and new examples of Banach spaces satisfying the fixed point p...

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Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) 2015-07, Vol.2015 (1), p.1-19, Article 109
Main Authors: Castillo-Santos, Francisco E, Japón, Maria A
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Banach space
Differential Geometry
Fixed points (mathematics)
Group theory
Mapping
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Theorems
Topology
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Summary:In this article we use the generalized Gossez-Lami Dozo property and the Opial condition to study the fixed point property for left reversible semigroups in separable Banach spaces. As a consequence, some previous results will be deduced and new examples of Banach spaces satisfying the fixed point property for left reversible semigroups are shown. We will also extend some previous theorems when we consider the semigroup formed by a unique nonexpansive mapping and its iterates.
ISSN:1687-1812
1687-1812
DOI:10.1186/s13663-015-0357-7