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Existence Results for Mixed Equilibrium Problems Involving Set-Valued Operators with Applications to Quasi-Hemivariational Inequalities

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Abstract

In this paper, we study the existence of solutions for mixed equilibrium problems associated with a set-valued operator in the general setting of vector spaces in duality, and in particular in Banach spaces. We use a Galerkin-type method and the notion of pseudomonotonicity in the sense of Brézis for bifunctions. As application, we study the existence of solutions for quasi-hemivariational inequalities governed by a set-valued mapping and perturbed with a nonlinear term. Our main results can be applied to differential inclusions, evolution equations and evolution hemivariational inequalities.

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Acknowledgements

The authors are very grateful to Professor Giannessi, Professor Ansari and the two anonymous reviewers for their constructive comments and valuable suggestions.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, 752050, India

    Bijaya Kumar Sahu & Sabyasachi Pani

  2. Department of Economics, Ibn Zohr University, B.P. 8658, Poste Dakhla, Agadir, Morocco

    Ouayl Chadli

  3. Department of Mathematics, University of Central Florida, Orlando, USA

    Ram N. Mohapatra

Authors
  1. Bijaya Kumar Sahu
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  2. Ouayl Chadli
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  3. Ram N. Mohapatra
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  4. Sabyasachi Pani
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Correspondence to Ouayl Chadli.

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Communicated by Qamrul Hasan Ansari.

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Sahu, B.K., Chadli, O., Mohapatra, R.N. et al. Existence Results for Mixed Equilibrium Problems Involving Set-Valued Operators with Applications to Quasi-Hemivariational Inequalities. J Optim Theory Appl 184, 810–823 (2020). https://doi.org/10.1007/s10957-019-01629-1

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