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Erschienen in:
2016 | OriginalPaper | Buchkapitel
4. Fixed Points for Maps with Weakly Sequentially Closed Graph
verfasst von : Afif Ben Amar, Donal O’Regan
Erschienen in: Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications
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Abstract
In this chapter, we discuss Sadovskii, Krasnoselskii, Leray–Schauder, and Furi–Pera type fixed point theorems for a class of multivalued mappings with weakly sequentially closed graph. We first discuss a Sadovskii type result for weakly condensing and 1-set weakly contractive multivalued maps with weakly sequentially closed graph. Next we discuss multivalued analogues of Krasnoselskii fixed point theorems for the sum S + T on nonempty closed convex of a Banach space where T is weakly completely continuous and S is weakly condensing (resp. 1-set weakly contractive). In particular we consider Krasnoselskii type fixed point theorems and Leray–Schauder alternatives for the sum of two weakly sequentially continuous mappings, S and T by looking at the multivalued mapping \((I - S)^{-1}T\), where I − S may not be injective. We note that the domains of all of the multivalued maps discussed here are not assumed to be bounded.