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Relative functional entropy in convex analysis
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Mustapha Raïssouli
Veröffentlicht/Copyright:
29. November 2011
Abstract
The purpose of this work is to extend the relative entropy
S(A|B) = A1/2 log(A–1/2BA–1/2)A1/2
from positive operators to convex functionals. Our functional approach implies immediately, in a fast way, some simplifications and improvements for that of positive operators already discussed in the literature.
Keywords.: Convex analysis; relative operator entropy; power harmonic operator and functional means; relative functional entropy
Received: 2009-10-28
Revised: 2010-04-27
Accepted: 2010-08-10
Published Online: 2011-11-29
Published in Print: 2011-December
© de Gruyter 2011
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Artikel in diesem Heft
- Oscillation criteria for a class of third-order nonlinear neutral differential equations
- Ellipses numbers and geometric measure representations
- Duals of homogeneous weighted sequence Besov spaces and applications
- On positive definite and stationary sequences with respect to polynomial hypergroups
- Relative functional entropy in convex analysis
- Damped wave equations with dynamic boundary conditions
- On Nemytskij operator in the space of absolutely continuous set-valued functions
Schlagwörter für diesen Artikel
Convex analysis;
relative operator entropy;
power harmonic operator and functional means;
relative functional entropy
Artikel in diesem Heft
- Oscillation criteria for a class of third-order nonlinear neutral differential equations
- Ellipses numbers and geometric measure representations
- Duals of homogeneous weighted sequence Besov spaces and applications
- On positive definite and stationary sequences with respect to polynomial hypergroups
- Relative functional entropy in convex analysis
- Damped wave equations with dynamic boundary conditions
- On Nemytskij operator in the space of absolutely continuous set-valued functions
