Displaying similar documents to “A resolution of Simon's maximal monotonicity problem.”

On super-weakly compact sets and uniformly convexifiable sets

Lixin Cheng, Qingjin Cheng, Bo Wang, Wen Zhang (2010)

Studia Mathematica

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This paper mainly concerns the topological nature of uniformly convexifiable sets in general Banach spaces: A sufficient and necessary condition for a bounded closed convex set C of a Banach space X to be uniformly convexifiable (i.e. there exists an equivalent norm on X which is uniformly convex on C) is that the set C is super-weakly compact, which is defined using a generalization of finite representability. The proofs use appropriate versions of classical theorems, such as James'...

Fixed point theorems for weakly sequentially closed maps

Donal O'Regan (2000)

Archivum Mathematicum

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A number of fixed point theorems are presented for weakly contractive maps which have weakly sequentially closed graph. Our results automatically lead to new existence theorems for differential inclusions in Banach spaces relative to the weak topology.