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On Variational Inequalities Involving Mappings of Type (S)

In: Nonlinear Analysis and Variational Problems

Author

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  • Dan Pascali

    (Courant Institute of Mathematical Sciences, New York University)

Abstract

Variational inequalities can be converted into inclusions defined by a sum between a mapping of monotone type and a subdifferential. In our case, a topological approach of variational inequalities is based on a degree function for a (S)-operator F with maximal monotone perturbations T. The paper surveys some new advances on topological degree in the case F+T, removing the condition 0∈T(0). In this way, the main difficulty is to determine the admissible homotopies. A graph homotopy for maximal monotone mappings is introduced. Finally, we mention some recent references regarding the related fixed point index.

Suggested Citation

  • Dan Pascali, 2010. "On Variational Inequalities Involving Mappings of Type (S)," Springer Optimization and Its Applications, in: Panos M. Pardalos & Themistocles M. Rassias & Akhtar A. Khan (ed.), Nonlinear Analysis and Variational Problems, chapter 0, pages 441-449, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-0158-3_27
    DOI: 10.1007/978-1-4419-0158-3_27
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