scholarly journals Characterization of Reflexivity by Convex Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-4
Author(s):  
Zhenghua Luo ◽  
Qingjin Cheng
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
Convexity Property ◽  
Reflexive Banach Spaces

A new convexity property of convex functions is introduced. This property provides, in particular, a characterization of the class of reflexive Banach spaces.

A characterization of essentially strictly convex functions on reflexive Banach spaces

2012 ◽  
Vol 75 (3) ◽  
pp. 1617-1622 ◽  
Author(s):  
Michel Volle ◽  
Jean-Baptiste Hiriart-Urruty
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
Reflexive Banach Spaces ◽  
Strictly Convex

scholarly journals A NEW CHARACTERIZATION OF REFLEXIVITY

2008 ◽  
Vol 78 (3) ◽  
pp. 443-444
Author(s):  
RUIDONG WANG
Keyword(s):  
Banach Spaces ◽  
Convex Sets ◽  
Reflexive Banach Spaces ◽  
Bounded Convex

AbstractIn this paper, we give a new characterization of reflexive Banach spaces in terms of the sum of two closed bounded convex sets.

scholarly journals A characterization of reflexive Banach spaces

1996 ◽  
Vol 124 (4) ◽  
pp. 1083-1090 ◽  
Author(s):  
Eva Matoušková ◽  
Charles Stegall
Keyword(s):  
Banach Spaces ◽  
Reflexive Banach Spaces

scholarly journals New Tour on the Subdifferential of Supremum via Finite Sums and Suprema

2021 ◽  
Author(s):  
A. Hantoute ◽  
M. A. López-Cerdá
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
Normal Cone ◽  
Countable Family ◽  
Weighted Sums ◽  
Reflexive Banach Spaces ◽  
Finite Dimensional ◽  
Finite Sums ◽  
Effective Domain ◽  
The Relationship

AbstractThis paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our formulas. Another aspect of our analysis is that it emphasizes the relationship with the subdifferential of the supremum of finite subfamilies, or equivalently, finite weighted sums. Some specific results are given in the setting of reflexive Banach spaces, showing that the subdifferential of the supremum can be reduced to the supremum of a countable family.

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