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Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations

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Abstract

By using some new developments in the theory of equilibrium problems, we study the existence of anti-periodic solutions for nonlinear evolution equations associated with time-dependent pseudomonotone and quasimonotone operators in the topological sense. More precisely, we establish new existence results for mixed equilibrium problems associated with pseudomonotone and quasimonotone bifunctions in the topological sense. The results obtained are therefore applied to study the existence of anti-periodic solutions for nonlinear evolution equations in the setting of reflexive Banach spaces. This new approach leads us to improve and unify most of the recent results obtained in this direction.

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Acknowledgments

The authors are gratefully indebted to the anonymous referee for his/her insightful comments that improved the paper. The research part of the second author was done during his visit to King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.

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Authors and Affiliations

  1. Department of Economics, Faculty of Economics and Social Sciences, Ibn Zohr University, B.P. 8658 Poste Dakhla, Agadir, Morocco

    Ouayl Chadli

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Qamrul Hasan Ansari

  3. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Qamrul Hasan Ansari

  4. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

  5. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Jen-Chih Yao

Authors
  1. Ouayl Chadli
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  2. Qamrul Hasan Ansari
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  3. Jen-Chih Yao
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Corresponding author

Correspondence to Qamrul Hasan Ansari.

Additional information

Communicated by Nicolas Hadjisavvas.

In this research, Jen-Chih Yao was partially supported by the research Grant 103-2923-E-037-001-MY3 of National Science Council of Taiwan.

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Chadli, O., Ansari, Q.H. & Yao, JC. Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations. J Optim Theory Appl 168, 410–440 (2016). https://doi.org/10.1007/s10957-015-0707-y

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  • DOI: https://doi.org/10.1007/s10957-015-0707-y

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