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Equilibrium Problems: Existence Results and Applications

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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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Authors and Affiliations

  1. Universidad del Pacífico, Av. Salaverry 2020, Jesús María, Lima, Perú

    John Cotrina & Yboon García

Authors
  1. John Cotrina
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  2. Yboon García
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Correspondence to Yboon García.

Additional information

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

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