Abstract
In this paper, we introduce certain regularizations for bifunctions, based on the corresponding regularization for functions, originally defined by J-P. Crouzeix. We show that the equilibrium problems associated to a bifunction and its regularizations are equivalent in the sense that they share the same solution set. Also, we introduce new existence results for the Equilibrium Problem, and we show some applications to minimization and Nash equilibrium problems.
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Acknowledgments
We would like to thank the anonymous referees for their valuable suggestions and remarks which allowed us to improve the original presentation of this paper. We are also greatly indebted to one of the referees for the proof of Proposition 3.10.
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This work was supported by Cienciactiva-Concytec EE020- MATH Amsud project nro.003-2017
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Cotrina, J., García, Y. Equilibrium Problems: Existence Results and Applications. Set-Valued Var. Anal 26, 159–177 (2018). https://doi.org/10.1007/s11228-017-0451-6
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DOI: https://doi.org/10.1007/s11228-017-0451-6
Keywords
- Equilibrium problems
- Convex feasibility problems
- Generalized monotonicity
- Generalized convexity
- Coercivity conditions
- Upper sign property
- Minimization problems
- Nash equilibrium problems