Differentiability of convex functions and the convex point of continuity property in Banach spaces

1987 ◽  
Vol 59 (2) ◽  
pp. 245-255 ◽  
Author(s):  
R. Deville ◽  
G. Godefroy ◽  
D. E. G. Hare ◽  
V. Zizler
1989 ◽  
Vol 32 (3) ◽  
pp. 274-280
Author(s):  
D. E. G. Hare

AbstractWe introduce a new type of differentiability, called cofinite Fréchet differentiability. We show that the convex point-of-continuity property of Banach spaces is dual to the cofinite Fréchet differentiability of all equivalent norms. A corresponding result for dual spaces with the weak* convex point-of-continuity property is also established.


1988 ◽  
Vol 37 (2) ◽  
pp. 263-271 ◽  
Author(s):  
R. Deville ◽  
G. Godefroy ◽  
D.E.G. Hare ◽  
V. Zizler

We show that if X is a separable Banach space such that X* fails the weak* convex point-of-continuity property (C*PCP), then there is a subspace Y of X such that both Y* and (X/Y)* fail C*PCP and both Y and X/Y have finite dimensional Schauder decompositions.


2011 ◽  
Vol 191 (1) ◽  
pp. 347-361 ◽  
Author(s):  
Ginés López Pérez ◽  
José A. Soler Arias

1993 ◽  
Vol 48 (1) ◽  
pp. 75-91 ◽  
Author(s):  
John R. Giles ◽  
Warren B. Moors

In a recent paper the authors showed that certain set-valued mappings from a Baire space into subsets of a Banach space which have a continuity property defined in terms of Kuratowski's index of non-compactness have inherent single-valued properties. Here we generalise the continuity property to one defined in terms of a weak index of non-compactness and we show that this wider class of set-valued mappings also has significant implications for the differentiability of convex functions on Banach spaces.


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