Non Convex Operators for Electromagnetic Geosounding Noise

2020 ◽  
Author(s):  
Hugo Hidalgo-Silva ◽  
E. Gomez-Trevino
Keyword(s):  
Convex Operators

Equicontinuity of Families of Convex and Concave-Convex Operators

1984 ◽  
Vol 36 (5) ◽  
pp. 883-898 ◽  
Author(s):  
Mohamed Jouak ◽  
Lionel Thibault
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Convex Functions ◽  
Positive Cone ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Convex Operator ◽  
Necessary And Sufficient ◽  
Convex Operators

J. M. Borwein has given in [1] a practical necessary and sufficient condition for a convex operator to be continuous at some point. Indeed J. M. Borwein has proved in his paper that a convex operator with values in an order topological vector space F (with normal positive cone F+) is continuous at some point if and only if it is bounded from above by a mapping which is continuous at this point. This result extends a previous one by M. Valadier in [16] asserting that a convex operator is continuous at a point whenever it is bounded from above by an element in F on a neighbourhood of the concerned point. Note that Valadier's result is necessary if and only if the topological interior of F+ is nonempty. Obviously both results above are generalizations of the classical one about real-valued convex functions formulated in this context exactly as Valadier's result (see for example [5]).

An ergodic theorem for convex operators

1983 ◽  
Vol 40 (1) ◽  
pp. 447-451 ◽  
Author(s):  
Gerd Rod�
Keyword(s):  
Ergodic Theorem ◽  
Convex Operators

Subdifferentials of convex operators

1978 ◽  
Vol 18 (5) ◽  
pp. 747-752 ◽  
Author(s):  
S. S. Kutateladze
Keyword(s):  
Convex Operators
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