scholarly journals DIFFERENTIABILITY OF QUASI-HOMOGENEOUS CONVEX AFFINE DOMAINS

2005 ◽  
Vol 42 (3) ◽  
pp. 485-498
Author(s):  
KYEONGHEE JO
Keyword(s):  
Homogeneous Convex

Characterization of the barrier parameter of homogeneous convex cones

1998 ◽  
Vol 81 (1) ◽  
pp. 55-76 ◽  
Author(s):  
Osman Güler ◽  
Levent Tunçel
Keyword(s):  
Convex Cones ◽  
Barrier Parameter ◽  
Homogeneous Convex

scholarly journals Symmetric homogeneous convex domains

1984 ◽  
Vol 93 ◽  
pp. 1-17
Author(s):  
Tadashi Tsuji
Keyword(s):  
Real Number ◽  
Convex Domain ◽  
Convex Cone ◽  
Affine Transformations ◽  
Convex Domains ◽  
Affine Line ◽  
Homogeneous Convex

Let D be a convex domain in the n-dimensional real number space Rn, not containing any affine line and A(D) the group of all affine transformations of Rn leaving D invariant. If the group A(D) acts transitively on D, then the domain D is said to be homogeneous. From a homogeneous convex domain D in Rn, a homogeneous convex cone V = V(D) in Rn+1 = Rn × R is constructed as follows (cf. Vinberg [11]):which is called the cone fitted on the convex domain D.

scholarly journals The Construction of Homogeneous Convex Cones

1966 ◽  
Vol 83 (2) ◽  
pp. 358 ◽  
Author(s):  
O. S. Rothaus
Keyword(s):  
Convex Cones ◽  
Homogeneous Convex

On Conjugate Convex Functions

1949 ◽  
Vol 1 (1) ◽  
pp. 73-77 ◽  
Author(s):  
W. Fenchel
Keyword(s):  
Convex Body ◽  
Convex Functions ◽  
Gauge Function ◽  
Conjugate Functions ◽  
Classical Work ◽  
Homogeneous Convex ◽  
The Way

Since the classical work of Minkowski and Jensen it is well known that many of the inequalities used in analysis may be considered as consequences of the convexity of certain functions. In several of these inequalities pairs of “conjugate” functions occur, for instance pairs of powers with exponents a and a related by 1/a + 1/a = 1. A more general example is the pair of positively homogeneous convex functions denned by Minkowski and known as the distance (or gauge) function and the function of support of a convex body. The purpose of the present paper is to explain the general (by the way rather elementary) idea underlying this correspondence.

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