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Vectorial Ekeland Variational Principles and Inclusion Problems in Cone Quasi‐Uniform Spaces

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Listed:
  • Jiang Zhu
  • Lei Wei
  • Yeol Je Cho
  • Cheng Cheng Zhu

Abstract

Some new vectorial Ekeland variational principles in cone quasi‐uniform spaces are proved. Some new equivalent principles, vectorial quasivariational inclusion principle, vectorial quasi‐optimization principle, vectorial quasiequilibrium principle are obtained. Also, several other important principles in nonlinear analysis are extended to cone quasi‐uniform spaces. The results of this paper extend, generalize, and improve the corresponding results for Ekeland′s variational principles of the directed vectorial perturbation type and other generalizations of Ekeland′s variational principles in the setting of F‐type topological space and quasi‐metric spaces in the literatures. Even in usual real metric spaces, some of our results are new.

Suggested Citation

  • Jiang Zhu & Lei Wei & Yeol Je Cho & Cheng Cheng Zhu, 2012. "Vectorial Ekeland Variational Principles and Inclusion Problems in Cone Quasi‐Uniform Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:310369
    DOI: 10.1155/2012/310369
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    References listed on IDEAS

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    1. Guang-Ya Chen & X. Yang & Hui Yu, 2008. "Vector Ekeland’s variational principle in an F-type topological space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 471-478, June.
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