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Does Kirk’s theorem hold for multivalued nonexpansive mappings?

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Autor: Domínguez Benavides, Tomás
Gavira Aguilar, Beatriz
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2010
Publicado en: Fixed Point Theory and Applications, 2010, 546761-1-546761-20.
Tipo de documento: Artículo
Resumen: Fixed Point Theory for multivalued mappings has many useful applications in Applied Sciences, in particular, in Game Theory and Mathematical Economics. Thus, it is natural to try of extending the known fixed point results for single-valued mappings to the setting of multivalued mappings. Some theorems of existence of fixed points of single-valued mappings have already been extended to the multivalued case. However, many other questions remain still open, for instance, the possibility of extending the well-known Kirk’s Theorem, that is: do Banach spaces with weak normal structure have the fixed point property FPP for multivalued nonexpansive mappings? There are many properties of Banach spaces which imply weak normal structure and consequently the FPP for single-valued mappings for example, uniform convexity, nearly uniform convexity, uniform smoothness,.... Thus, it is natural to consider the following problem: do these properties also imply the FPP for multivalued mappings? In this ...
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Cita: Domínguez Benavides, T. y Gavira Aguilar, B. (2010). Does Kirk’s theorem hold for multivalued nonexpansive mappings?. Fixed Point Theory and Applications, 2010, 546761-1-546761-20.
Tamaño: 266.5Kb
Formato: PDF

URI: http://hdl.handle.net/11441/49083

DOI: 10.1155/2010/546761

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