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165. Fan-hemicontinuity for the gradient of the norm in several reflexive Banach spaces
Invited abstract in session WB-43: Recent advances on Variational Inequalities and Equilibrium Problems I, stream Variational Inequalities and Equilibrium Problems: From Theoretical Advances to Real World Applications.
Wednesday, 10:30-12:00Room: 99 (building: 306)
Authors (first author is the speaker)
| 1. | Marcel Bogdan
|
| Department of Industrial Engineering and Management, George Emil Palade University of Medicine, Phaamacy, Science, and Technology of Targu Mures |
Abstract
The present study approaches variational inequalities governed by the perturbed operator generated by the energy of the mathematical pendulum. It was proved recently Fan-hemicontinuity for the gradient of the norm defined on its scalarly-positive, closed convex subdomain of a Hilbert space. The aim of the present study is to establish whether or not the positive result obtained for Fan-hemicontinuity can be extended to an arbitrary reflexive Banach space. In this matter it is natural to consider the duality map and its topological properties. Based on weak-weak sequential continuity of the generalized duality map, the property above holds on the discrete spaces of sequences with power p summable and does not hold on the Lebsegue spaces of functions with power p integrable, (p not equal to 2), thus restricting the space setting where weak compactness results are applicable.
Keywords
- Convex Optimization
- Continuous Optimization
- Global Optimization
Status: accepted
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