Periodica Mathematica Hungarica

, Volume 33, Issue 2, pp 83–92 | Cite as

Ekeland's variational principle and Caristi's coincidence theorem for set-valued mappings in probabilistic metric spaces

  • Shih-sen Chang
  • Yeol Je Cho
  • Jong Kyu Kim


By using the partial ordering method, a more general type of Ekeland's variational principle and Caristi's coincidence theorem for set-valued mappings in probabilistic metric spaces are given in this paper. In addition, we give also a directly simple proof of the equivalence between theses theorems in probabilistic metric spaces.

Mathematics subject classification numbers, 1991

Primary 47H10 34H25 

Key words and phrases

A distribution function at-norm a Menger PM-space Caristi's coincidence theorem Ekeland's variational principle 


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Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • Shih-sen Chang
    • 1
  • Yeol Je Cho
    • 2
  • Jong Kyu Kim
    • 3
  1. 1.Department of MathematicsSichuan UniversityChengdu, SichuanPeople's Republic of China
  2. 2.Department of MathematicsGyeongsang National UniversityChinjuKorea
  3. 3.Department of MathematicsKyungnam UniversityMasanKorea

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