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Acta Mathematica Scientia

, Volume 39, Issue 2, pp 524–544 | Cite as

Vectorial Ekeland Variational Principle and Cyclically Antimonotone Equilibrium Problems

  • Jinghui QiuEmail author
Article
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Abstract

In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle (see Qiu, 2014), we prove a new version of Ekeland variational principle (briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results (no matter scalar-valued case, or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings.

Key words

equilibrium problem cyclic antimonotonicity vectorial Ekeland variational principle sequentially compact topological space countably compact topological space 

2010 MR Subject Classification

49J53 58E30 91B50 

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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesSoochow UniversitySuzhouChina

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