scholarly journals Two Characterizations of Super-Reflexive Banach Spaces by the Behaviour of Differences of Convex Functions

2002 ◽  
Vol 191 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Manuel Cepedello Boiso
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
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 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.

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.

scholarly journals Generalised second-order derivatives of convex functions in reflexive Banach spaces

1995 ◽  
Vol 51 (1) ◽  
pp. 55-72 ◽  
Author(s):  
James Louis Ndoutoume ◽  
Michel Théra
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
Quadratic Forms ◽  
Second Order ◽  
Second Derivative ◽  
Reflexive Banach Spaces ◽  
Finite Dimensional ◽  
Derivatives Of

Generalised second-order derivatives introduced by Rockafellar in the finite dimensional setting are extended to convex functions defined on reflexive Banach spaces. Our approach is based on the characterisation of convex generalised quadratic forms defined in reflexive Banach spaces, from the graph of the associated subdifferentials. The main result which is obtained is the exhibition of a particular generalised Hessian when the function admits a generalised second derivative. Some properties of the generalised second derivative are pointed out along with further justifications of the concept.

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